Water Diffusion in Bicelles and the Mixed Bicelle Model - American

Dec 8, 2008 - UniVersity of Toronto Mississauga, 3359 Mississauga Road North, Mississauga, Ontario, Canada L5L 1C6. ReceiVed June 4, 2008. ReVised ...
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Langmuir 2009, 25, 380-390

Water Diffusion in Bicelles and the Mixed Bicelle Model Ronald Soong and Peter M. Macdonald* Department of Chemistry, UniVersity of Toronto, and Department of Chemical and Physical Sciences, UniVersity of Toronto Mississauga, 3359 Mississauga Road North, Mississauga, Ontario, Canada L5L 1C6 ReceiVed June 4, 2008. ReVised Manuscript ReceiVed September 11, 2008 To test a prediction of the mixed bicelle model, stimulated echo (STE) pulsed field gradient (PFG) 1H nuclear magnetic resonance (NMR) measurements of water diffusion between and across bicellar lamellae were performed in positively and negatively magnetically aligned bicelles, composed of mixtures of DHPC (1,2-dihexanoyl-snglycero-3-phosphocholine) and DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine), as a function of temperature and of the proportion of added short-chain lipid DHPC. 31P NMR spectra obtained for each situation confirmed that the DHPC undergoes fast exchange between curved and planar regions as per the mixed bicelle model and permitted an estimate of the proportion of the two DHPC populations. Water diffusion across the bicellar lamellae was shown to scale directly with q*, the fraction of edge versus planar phospholipid, rather than simply the ratio q, the global fraction of long-chain to short-chain phospholipid. Geometric modeling of the dependence of water diffusion on q* suggested an upper limit of 400 Å for the size of DHPC-rich toroidal perforations within the bicelle lamellae. These findings constitute an independent confirmation of the mixed bicelle model in which DHPC is not confined to edge regions but enjoys, instead, a finite miscibility with DMPC.

Introduction Bicelles, or bilayered micelles, are widely employed as model membranes in biophysical studies of the conformation and dynamics of membrane-associating molecules,1-5 including membrane proteins.6 They are likewise useful as an anisotropic alignment medium, yielding NMR-observable residual dipolar couplings for soluble biomacromolecules present within the aqueous space between bicelles, thereby providing additional constraints in NMR structure determinations of such species.7 Bicelles consist of mixtures of short-chain amphiphiles, typically DHPC (1,2-dihexanoyl-sn-glycero-3-phosphocholine), and long-chain amphiphiles, typically DMPC (1,2-dimyristoylsn-glycero-3-phosphocholine). This archetypal DHPC + DMPC bicellar mixture was first introduced by Sanders and Schwonek.8 The long-chain amphiphiles self-assemble into planar bilayers, while the short-chain amphiphiles segregate to edge regions of high curvature. Bicelles have the particular property that they spontaneously align in the magnetic field of an NMR spectrometer over a wide range of values of the molar ratio q ) DMPC/ DHPC, temperature, pH, ionic strength, and water content. The alignment is driven by the interaction between the magnetic field and the magnetic susceptibility anisotropy of the bicellar selfassembly, aided by cooperative interactions between adjacent lamellae.9 For DMPC/DHPC bicelles, because of their net negative magnetic susceptibility anisotropy, the spontaneous direction of alignment is such that the normal to the planar lipid bilayer region lies perpendicular to the direction of the magnetic * To whom correspondence should be addressed. Tel.: 905 828 3805. Fax: 905 828 5425. E-mail: [email protected]. (1) Sanders, C. R.; Hare, B. J.; Howard, K. P.; Prestegard, J. H. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 421–444. (2) Sanders, C. R.; Prosser, R. S. Structure 1998, 16, 1227–1234. (3) Marcotte, I.; Auger, M. Concepts Magn. Reson. 2005, 24A, 17–37. (4) Katsaras, J.; Harroun, T. A.; Pencer, J.; Nieh, M. P. Naturwissenschaften 2005, 92, 355–366. (5) Prosser, R. S.; Evanics, F.; Kitevski, J. L.; Al-Abdul-Wahid, M. S. Biochemistry 2006, 45, 8453–8465. (6) Howard, K. P.; Opella, S. J. J. Magn. Reson., Ser. B 1996, 112, 91–94. (7) Tjandra, N.; Bax, A. Science 1997, 278, 1111–1114. (8) Sanders, C. R.; Schwonek, J. P. Biochemistry 1992, 31, 8898–8905. (9) Boroske, E.; Helfrich, W. Biophys. J. 1978, 24, 863–868.

field. This is referred to as negative magnetic alignment. As first reported by Prosser and Vold and co-workers,10-12 in the presence of surface-bound lanthanides having a positive magnetic susceptibility, such as Tm3+, Yb3+, Er3+, and Eu3+, the direction of alignment is such that the normal to the planar lipid bilayer region lies parallel to the direction of the magnetic field. This is referred to as positive magnetic alignment and is particularly useful for solid-state NMR studies of membrane proteins. A consensus regarding bicelle morphology has emerged from a combination of NMR,13-16 small-angle X-ray scattering (SAXS),17 small-angle neutron scattering (SANS),4,18-22 fluorescence,23 and electron microscopy16,24,25 observations. At q < 2, or at temperatures below the DMPC gel-to-liquid-crystalline phase transition (Tm), bicelles do not magnetically align and, structurally, appear discoidal with DHPC ringing the edges of a DMPC bilayer disk. At q g 2, and at temperatures just above the Tm of DMPC, negatively magnetically aligned bicelles adopt (10) Prosser, R. S.; Hunt, S. A.; DiNatale, J. A.; Vold, R. R. J. Am. Chem. Soc. 1996, 118, 269–270. (11) Prosser, R. S.; Bryant, H.; Bryant, R. G.; Vold, R. R. J. Magn. Reson. 1999, 141, 256–260. (12) Prosser, R. S.; Shiyanovskaya, I. V. Concepts Magn. Reson. 2001, 13, 19–31. (13) Ottinger, M.; Bax, A. J. Biomol. NMR 1998, 12, 361–372. (14) Raffard, G.; Steinbruckner, S.; Arnold, A.; Davis, J. H.; Dufourc, E. J. Langmuir 2000, 16, 7655–7662. (15) Sternin, E.; Nizza, D.; Gawrisch, K. Langmuir 2001, 17, 2610–2616. (16) Arnold, A.; Labrot, T.; Oda, R.; Dufourc, E. J. Biophys. J. 2002, 83, 2667–2680. (17) Boltze, J.; Fujisawa, T.; Nagao, T.; Norisada, K.; Saito, H.; Naito, A. Chem. Phys. Lett. 2000, 329, 215–220. (18) 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. (19) Nieh, M. P.; Glinka, C. J.; Krueger, S.; Prosser, R. S.; Katasaras, J. Langmuir 2001, 17, 2629–2638. (20) Nieh, M. P.; Glinka, C. J.; Krueger, S.; Prosser, R. S.; Katasaras, J. Biophys. J. 2002, 82, 2487–2498. (21) Nieh, M. P.; Raghunathan, V. A.; Glinka, C. J.; Harroun, T. A.; Pabst, G.; Katsaras, J. Langmuir 2004, 20, 7893–7897. (22) Harroun, T. A.; Koslowsky, M.; Nieh, M. P.; de Lannoy, C. F.; Raghunathan, V. A.; Katsaras, J. Langmuir 2005, 21, 5356–5361. (23) Rowe, B. A.; Neal, S. L. Langmuir 2003, 19, 2039–2048. (24) Van Dam, L.; Karlsson, G.; Edwards, K. Biochim. Biophys. Acta 2004, 1664, 241–256. (25) Van Dam, L.; Karlsson, G.; Edwards, K. Langmuir 2006, 22, 3280–3285.

10.1021/la801739a CCC: $40.75  2009 American Chemical Society Published on Web 12/08/2008

Water Diffusion in Bicelles

Figure 1. Schematic representation of the perforated lamellae morphology of magnetically aligned DMPC/DHPC bicelles. DMPC (green) is assumed to segregate to planar regions while DHPC (red) prefers edge regions of high curvature, yielding DHPC-rich toroidal perforations decorating the DMPC-rich planar lamellae. The mixed bicelle model posits that DHPC is finitely miscible with DMPC, undergoing a rapid exchange between, and in equilibrium with, DHPC populations occupying curved and planar regions (ref 27). Because the bicellar lamellae act as obstructions to diffusion, diffusion of small molecules trapped within the interstices between adjacent lamellae is anisotropic with tensor components D| and D⊥, corresponding to diffusion parallel and perpendicular to the bilayer normal, as indicated in the figure. D| will depend most sensitively on the surface fraction of toroidal perforations, assuming they are large relative to the size of the particular diffusant. According to the mixed bicelle model, this surface fraction of “holes” should vary as the fraction of DHPC resident in curved regions, as opposed to simply the global DMPC/DHPC ratio. Hence, measurements of D| provide a means of independently testing the mixed bicelle model.

a chiral nematic phase consisting of DMPC-rich broad ribbons having their edges coated with DHPC.21 The presence of a negatively charged lipid like dimyristoyl phosphatidylglycerol (DMPG), however, prompts a morphology consisting of DMPC + DMPG-rich lamellar sheets perforated by toroidal holes lined with DHPC.25 Likewise, in positively magnetically aligned bicelles the perforated lamellar morphology is predominant, a schematic representation of which is shown in Figure 1. Despite this progress a number of questions concerning bicelle morphology remain to be resolved. One concerns the size of, and spacing between, the DHPC-enriched toroidal defects which, because they exhibit no long-range order, are not amenable to characterization by SANS. They can be visualized via cryotransmission electron microscopy (cryo-TEM),25 but subject to the usual provisos regarding perturbation by the sample preparation technique. The commonly used NMR techniques for characterizing bicelles do not readily provide such information: a single 31P or 2H NMR spectrum, for instance, does not differentiate between aligned discoidal versus ribbons versus perforated lamellar morphologies. Entangled with the above question is the issue of whether, and to what degree, DHPC remains segregated to edge regions of high curvature. It was early hypothesized that a strict segregation between DHPC and DMPC prevailed, leading to the “ideal

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bicelle” model of Vold and Prosser.26 This has been challenged recently on the basis of detailed 31P NMR studies of bicellar mixtures as a function of temperature and molar ratio q by Triba et al.27 These researchers proposed, instead, a “mixed bicelle” model in which DHPC is finitely miscible with DMPC, as indicated in Figure 1, and increasingly so with increasing temperature above the Tm of DMPC. This notion has been supported by molecular dynamics simulations28 and has received independent experimental confirmation using 31P NMR and cryoTEM.25 A consequence of the mixed bicelle model is that the number and spacing, if not the size, of toroidal perforations formed by DHPC should be dependent upon the fraction of DHPC resident in edge versus lamellar regions, as distinct from simply the global molar ratio q ) DMPC/DHPC. An independent test of this prediction of the mixed bicelle model could be provided by measuring water diffusion through the toroidal perforations or defects assumed to be formed by DHPC using, for example, the pulsed field gradient (PFG) NMR diffusion technique. First introduced by Stejskal and Tanner,29 the PFG NMR diffusion technique has long been used to provide fundamental morphological information on colloidal systems.30-33 In particular, spatial restrictions reduce the selfdiffusion coefficients of tracer molecules when measured over length scales exceeding that characteristic of the obstructions. The degree of restriction, or lack of it, and any anisotropy of self-diffusion reveals structural information on the obstructing geometry. For the specific case of magnetically aligned bicelles in the perforated lamellar morphology, which will be of most interest here, diffusion of water in the direction parallel to the bicelle normal should be obstructed essentially completely by planar lamellar regions but should be virtually unrestricted through the DHPC-rich toroidal perforations, assuming they are large in size relative to a water molecule. Again, Figure 1 represents this situation schematically. Thus, water diffusion parallel to the bicelle normal should be a particularly sensitive indicator of the number and size and spacing of the DHPC-rich toroidal perforations in the DMPC-rich lamellae regions. An analogous experiment has been performed by Gaemers and Bax,34 who sought to characterize the morphology of three different lyotropic liquid-crystalline NMR alignment media via analysis of the observed anisotropy of water diffusion, concluding that their bicellar mixtures assumed a perforated lamellar morphology. These measurements were performed on negatively magnetically aligned bicelles so that, although the bicelle normal throughout the sample is uniformly perpendicular to the principal magnetic field direction, within the plane perpendicular to the principal magnetic field the direction of the bicelle normals is distributed cylindrically. Consequently, water diffusion in the direction across the bicellar lamellae can only be measured indirectly upon comparing results obtained for the cases of field gradients applied in directions parallel and perpendicular to the principal magnetic field. A more straightforward means of measuring water diffusion across bicellar lamellae would be to employ positively magnetically aligned bicelles, wherein the bicelle normals are uniformly aligned in a direction parallel to the principal magnetic field. The (26) Vold, R. R.; Prosser, R. S. J. Magn. Reson., Ser. B 1996, 113, 267–271. (27) Triba, M. N.; Warschawski, D. E.; Devaux, P. E. Biophys. J. 2005, 88, 1887–1901. (28) Jiang, Y.; Kindt, J. T. J. Chem. Phys. 2007, 126, 0451051–0451059. (29) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288–295. (30) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1–45. (31) Ka¨rger, J.; Pfeifer, H.; Heink, W. AdV. Magn. Opt. Reson. 1988, 12, 1–89. (32) Price, W. S. Concepts Magn. Reson. 1997, 9, 299–336. (33) Price, W. S. Concepts Magn. Reson. 1998, 10, 197–237. (34) Gaemers, S.; Bax, A. J. Am. Chem. Soc. 2001, 123, 12343–12352.

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PFG NMR diffusion experiment with field gradients directed parallel to the principal magnetic field then directly measures water diffusion across the bicellar lamellae. We report here PFG NMR measurements of water diffusion across bicellar lamellae in positively magnetically aligned bicelles. Our goal is to test the predictions of the mixed bicelle model for such water diffusion as expected upon varying the molar ratio q and the temperature. For reference purposes, and to characterize the diffusional anisotropy, we performed identical PFG NMR water diffusion experiments on negatively magnetically aligned bicelles. To confirm that our bicelle samples, both positively and negatively magnetically aligned, behave according to the precepts of the mixed bicelle model proposed by Triba et al.,27 we examined all bicelle samples using 31P NMR, which allows us to assess the quality of magnetic alignment and to quantify the mole fraction of DHPC resident in edge versus planar regions. We demonstrate herein that translamellar water diffusion in bicelles is a direct function of the DHPC fraction resident in edge regions, thereby confirming a prediction following directly from the mixed bicelle model. Geometric modeling of the assumed DHPC-lined lamellar defects then provides an upper bound on their size based on the observed translamellar water diffusion coefficient.

Experimental Section Materials. DMPC, DHPC, DMPG (1,2-dimyristoyl-sn-glycero3-phosphoglycerol), and DMPE-PEG2000 (1,2-dimyristoyl-snglycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)2000]) were purchased from Avanti Polar Lipids, Alabaster, AL. Ytterbium chloride hexahydrate (YbCl3(6H2O)) was purchased from Sigma-Aldrich, Oakville, ON, Canada, as were all other biochemicals and reagents employed. Bicelle Preparation. Bicelles for positive magnetic alignment were prepared to consist of 25 wt % lipid in 450 µL of buffered H2O/D2O (10/90 v/v) containing a prescribed quantity of Yb3+. The ratio q, being the molar ratio of long- to short-chain lipids, was calculated as moles of (DMPC + DMPG + DMPE-PEG2000)/ moles of DHPC, where the long-chain amphiphiles included DMPC plus 5 mol % DMPG plus 1 mol % DMPE-PEG2000, the latter two mol % being held constant and calculated relative to 100 mol % DMPC. A typical preparation involved hydrating the desire quantity of DMPC, DHPC, DMPG, and DMPE-PEG2000 with 350 µL of buffered H2O/D2O solution (10 mM Tris, pH 7.4, 150 mM NaCl), followed by a series of cycles of freezing, thawing, and gentle vortexing until a clear solution was obtained. To this clear solution, the desired quantity of Yb3+ was introduced from a stock solution, [Yb3+] ) 10 mg/mL, such that the final volume of the bicelle solution was 450 µL and the ratio of Yb3+/P was 1:75. The solution was then stored at 4 °C for up to 24 h before use. For negatively magnetically aligned bicelles DMPE-PEG2000 and Yb3+ were omitted entirely. Magnetic Alignment of Bicelles. The bicellar mixture was transferred into a 5 mm NMR sample tube at 4 °C and placed in the bore of a 500 MHz NMR spectrometer. The sample temperature was then raised to 35 °C. An annealing procedure was carried out involving repeated cycling of the temperature between 20 and 35 °C with 10-15 min of equilibration at either extreme to encourage magnetic alignment. The quality of the magnetic alignment was assessed via 31P NMR spectroscopy. NMR Spectroscopy. All NMR spectra were recorded on a Varian Infinity 500 MHz NMR spectrometer using a Varian 5 mm double-resonance liquid probe equipped with gradient coils along the z-direction. The sample temperature was controlled to the desired value, between 25 and 45 °C, ( 0.5 °C, as calibrated separately using ethylene glycol as an NMR thermometer.35 31P NMR spectra were recorded at 202.31 MHz using a single-pulse excitation, quadrature detection, complete phase cycling of the pulses, and WALTZ proton decoupling during the signal acquisition with a proton decoupler field strength of 2 kHz. Typical

Soong and Macdonald acquisition parameters are as follows: a 90° pulse length of 3.7 µs, a recycle delay of 3 s, a spectral width of 100 kHz, and an 8K data size. Spectra were processed with an exponential multiplication equivalent to 50 Hz line broadening prior to Fourier transformation and were referenced to 85% phosphoric acid. 1 H NMR diffusion measurements were performed at 499.78 MHz using the stimulated echo (STE) pulsed field gradient (PFG) procedure,36 with square gradient pulses of constant duration (5 ms) and variable gradient pulse amplitude, directed along the longitudinal (z) axis exclusively. Typical acquisition parameters are as follows: a 90° pulse length of 16 µs, a spin echo delay of 10 ms, a stimulated echo delay between 100 and 600 ms, a recycle delay of 5 s, a spectral width of 10 kHz, and a 4K data size. The phases of the radio frequency pulses were cycled to eliminate unwanted echoes.37 Spectra were processed with an exponential multiplication equivalent to 5 Hz line broadening prior to Fourier transformation and were referenced to external tetramethylsilane (TMS). Gradient strength was calibrated from the known diffusion coefficient of HDO in D2O at 25 °C (D0 ) 1.9 × 10-9 m2 s-1).38 Proton T1 relaxation times were measured using a standard inversion recovery protocol.

Results and Discussion 31

P NMR Spectra of Bicelles as a Function of q and Temperature. Before embarking on diffusion measurements it is essential to assess the quality of the bicelle alignment, and 31P NMR spectroscopy provides a convenient means of doing so. Figure 2A shows a series of 31P NMR spectra of Yb3+-doped, positively magnetically aligned bicelles at various q values from 3.5 to 6.5, all obtained at 35 °C. At low q two resonances are resolved. The broader resonance at roughly 20 ppm is assigned to DMPC, since this frequency corresponds to the chemical shift of the high-frequency shoulder in the 31P NMR powder spectrum of nonoriented liquid-crystalline DMPC bilayers, where the bilayer normal is oriented at 0° relative to the magnetic field. Hence, this resonance is consistent with a population of lipids occupying a planar lipid bilayer region preferentially oriented with its bilayer normal parallel to the magnetic field direction, as anticipated in the presence of a positive magnetic susceptibility anisotropy due to surface-bound Yb3+. The narrower resonance at roughly 5 ppm is assigned to DHPC by default and from the correlation of its integrated intensity with that expected given the particular q. The smaller chemical shift exhibited by DHPC is consistent with a fast exchange between populations preferentially occupying regions of high curvature but capable of infiltrating planar regions, as per the interpretation of Triba et al.27 Separate 31P NMR resonances for DMPG and DMPEPEG2000 were not evident in these spectra. This is not unanticipated, since both of these latter phospholipids are present in relatively small amounts (5 and 1 mol %, respectively) and should exhibit chemical shifts not radically different from that of DMPC. With increasing q the chemical shift of the DMPC resonance progressively increases (see Table 1 for details). This is a manifestation of the well-known scaling of the bicelle order parameter Sbicelle with q, where increasing DHPC (decreasing q) decreases bicelle ordering.1 The order parameter Sbicelle quantifies the additional local “wobbling” experienced by a phospholipid resident within a bicelle relative to a nonoriented bilayer and is (35) Ammann, C.; Meier, P.; Mebach, A. E. J. Magn. Reson. 1982, 46, 319– 321. (36) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523–2526. (37) Fauth, J. M.; Schweiger, A.; Braunschweiler, L.; Forrer, J.; Ernst, R. R. J. Magn. Reson. 1986, 66, 74–85.

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Figure 2. 31P NMR spectra of (A) positively magnetically aligned bicelles composed of 100/5/1 (mol/mol/mol) DMPC/DMPG/DMPE-PEG2000 + DHPC in the ratio q ) (DMPC + DMPG + DMPE-PEG2000)/DHPC as indicated in the figure and (B) negatively aligned bicelles composed of 100/5 (mol/mol) DMPC/DMPG + DHPC in the ratio q ) (DMPC + DMPG)/DHPC as indicated in the figure. Positively magnetically aligned bicelles included ytterbium in the ratio Yb3+/P ) 1/75. Negatively magnetically aligned bicelles lacked ytterbium. All samples contained 25% w/w/lipid/water, and all spectra were acquired at 35 °C. The various chemical shifts of the observed resonances are listed in Tables 1 and 2 for the spectra in (A) and (B), respectively.

derived from the 31P NMR residual chemical shift anisotropy of DMPC as described by Sanders et al.1

δobs - δiso Sbicelle ) δ0 - δiso

chemical shift (ppm)b,c

(1)

where δobs is the observed 31P NMR chemical shift of the positively magnetically aligned bilayers relative to the isotropic chemical shift δiso, while δ0 is the chemical shift of the 0°, i.e., higher frequency, shoulder in the 31P NMR powder spectrum of corresponding nonoriented bilayers such as multilamellar vesicles (MLV). For the spectra shown in Figure 2A, Sbicelle increases from 0.5 to 0.8 as q increases from 3.5 to 6.5. The DHPC resonance exhibits an even more pronounced shift to higher frequencies with increasing q, eventually overlapping the DMPC resonance for q ) 6.5. This is, again, essentially identical to the findings of Triba et al.27 who interpreted this as indicating that the fraction of DHPC within the planar bilayer (38) Mills, R. J. Phys. Chem. 1973, 77, 685–688.

Table 1. 31P NMR Chemical Shifts as a Function of q ) (DMPC + DMPG + DMPE-PEG2000)/DHPC for Positively Magnetically Aligned Bicellesa

q

DMPC

DHPCd

q* ) (q + ω*)/ (1 - ω*)e

3.5 4.5 5.5 6.5

17.3 19.7 20.9 22.0

7.4 9.4 11.1 13.6

6.9 9.5 12.9 18.6

a 100/5/1 (mol/mol/mol) DMPC/DMPG/DMPE-PEG2000 + DHPC as indicated by q, Yb3+/P ) 1/75, 25% w/w lipid/water, 35 °C. b Relative to 85% phosphoric acid. c DMPG and DMPE-PEG2000 resonances could not be resolved in the presence of Yb3+. d From MestreC line fitting in cases of q ) 5.5 and 6.5. e ω* ) ωDHPC/ωDMPC

regions, relative to the fraction within regions of high curvature, increases with increasing q. In the absence of Yb3+ the bicelles have a negative magnetic susceptibility anisotropy and so spontaneously magnetically align with the normal to the planar bilayer oriented at 90° relative to the magnetic field direction. Examples of the resulting 31P NMR

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Table 2. 31P NMR Chemical Shifts as a Function of q ) (DMPC + DMPG)/DHPC for Negatively Magnetically Aligned Bicellesa chemical shift (ppm)b q

DMPC

DMPG

DHPC

q* ) (q + ω*)/ (1 - ω*)c

ellipticity r ) c/ad

3.5 4.5 5.5 6.5

-11.2 -12.1 -12.5 -13.3

-7.5 -8.2 -8.9 n.d.

-4.2 -5.0 -6.2 -8.0

6.2 8.4 11.9 17.8

4.0 3.3

a 100/5 (mol/mol) DMPC/DMPG + DHPC as indicated by q, Yb3+/P ) 0, 25% w/w lipid/water, 35 °C. b Relative to 85% phosphoric acid. c ω* ) ωDHPC/ωDMPC. d From line shape fitting as per Picard et al. (ref 39) for the cases q ) 5.5 and 6.5.

spectra at 35 °C are shown in Figure 2B for the same q values as in Figure 2A. At q equal to 3.5 or 4.5, the DMPC, DHPC, and DMPG resonances are quite narrow and well-resolved. The DMPC resonance occurs at roughly -12 ppm, corresponding to the 90° shoulder in the 31P NMR powder spectrum of nonoriented liquid-crystalline DMPC bilayers, whereas the DHPC resonance occurs at roughly -5 ppm. The small DMPG resonance appears at roughly -9 ppm. Details are provided in Table 2. At these q values the quality of the negative magnetic alignment of these bicelles is quite satisfactory. Upon increasing q to 5.5 and 6.5 for these negatively magnetically aligned bicelles, the 31P NMR resonances continue to shift progressively to lower frequencies, with DHPC again exhibiting the most profound changes. The increase in Sbicelle with increasing q observed for the negatively magnetically aligned bicelles is similar, if not identical, to that observed with positively magnetically aligned bicelles. Simultaneously, the spectra reflect a progressively less uniform bicelle alignment. At q ) 5.5 this is manifest in the form of broader resonance lines, whereas at q ) 6.5 the spectrum exhibits characteristics indicative of an ellipsoidal distribution of local orientations. Such results conform to those first reported by Triba et al.27 in their detailed examination of q and temperature effects in 31P NMR spectra of similar bicellar mixtures. These authors attributed such effects to a progressive tendency of DHPC to migrate into planar bicelle regions, upon which basis they proposed their mixed bicelle model. Eventually a transformation from planar to ellipsoidal structures occurs with increasing q. Spectra for cases of less-than-ideal alignment may be simulated using the line shape functions derived by Picard et al.39 for an ellipsoidal distribution of the bicelle normal as a function of the eccentricity r ) c/a of the ellipsoid, where for negative magnetic alignment c and a are the lengths of the ellipsoid’s semimajor and semiminor axes, respectively, assuming the major axis is oriented parallel to the principal magnetic field. Using eq 12 of Picard et al.39 and assuming the standard 31P chemical shift anisotropy of 45 ppm for DMPC in a liquid-crystalline environment, we were able to simulate both the q equal to 5.5 and 6.5 31 P NMR spectra, yielding apparent ellipsoidal eccentricities of r ) c/a equal to 4.0 and 3.3, respectively. When the positively magnetically aligned bicelles in the presence of Yb3+ are compared with the negatively magnetically aligned bicelles in the absence of Yb3+, it is evident that markedly narrower line widths are obtained in the absence of Yb3+, as per Figure 2B, relative to its presence, as per Figure 2A. This is directly a manifestation of paramagnetic broadening induced by this lanthanide. It is apparent, nevertheless, that the positive magnetic susceptibility produced by Yb3+ binding to the bicelle surface encourages and produces a high-quality of magnetic (39) Picard, F.; Paquet, M. J.; Levesque, J.; Belanger, A.; Auger, M. Biophys. J. 1999, 77, 888–902.

alignment over a wider range of q values than it is possible to obtain in the absence of Yb3+ under otherwise identical conditions. Temperature is another major factor influencing bicelle morphology and quality of magnetic alignment. Figure 3A shows a series of 31P NMR spectra of q ) 4.5, Yb3+-doped, bicelles at temperatures of 25, 30, 35, and 40 °C. Positive magnetic alignment of this bicelle sample was achieved via the annealing procedure described in the Experimental Section prior to acquiring the spectra shown in Figure 3A. At 25 °C, just above the gelto-liquid-crystalline phase transition of DMPC, the relatively broad DMPC resonance exhibits a chemical shift of 16.7 ppm, consistent with a positive magnetic alignment of liquid-crystalline phospholipid. The DHPC resonance, in contrast, is quite narrow and exhibits a chemical shift near the isotropic value. This indicates a virtually complete phase separation of DMPC and DHPC into planar and highly curved regions, respectively, at this temperature. With increasing temperature the DMPC chemical shift moves to somewhat higher frequencies, reaching 18.3 ppm at 40 °C. In contrast, the DHPC resonance shifts dramatically to higher frequencies over the same temperature range, increasing to 11.7 ppm at 40 °C and overlapping with the DMPC resonance. Details are provided in Table 3. Again, these findings conform to those reported by Triba et al.27 who interpreted such results as indicating that the miscibility of DHPC with DMPC increases profoundly with increasing temperature over this range. In the presence of Yb3+, this occurs without, in so doing, compromising the overall positive magnetic alignment of the planar regions of the bicelle self-assembly. Concomitantly, the proportion of highly curved regions must decrease as DHPC invades the planar DMPCrich regions. Note that the spectra give no indication of any conversion of these positively magnetically aligned bicelles to a multilamellar phase or any other less-than-desirable-for-ourpurposes morphology, such as those known to prevail at higher temperatures.19,20 As shown in Figure 3B, over the same temperature range, the 31 P NMR spectra of q ) 4.5 negatively magnetically aligned bicelles, i.e., lacking added Yb3+, likewise maintain their magnetic alignment. The chemical shifts of the various phospholipid components vary with temperature in more-or-less the fashion one would predict from the dependence observed with the positively magnetically aligned bicelles, including the rather pronounced migration of DHPC from a nearly isotropic chemical shift at 25 °C to one much nearer that of DMPC at 40 °C. Tables 1-4 summarize the 31P NMR chemical shifts for both the positively and negatively magnetically aligned bicelles at these various q values and temperatures. The most profound changes are in the chemical shift of DHPC, and these may be interpreted in terms of the mixed bicelle model which posits that DHPC undergoes fast exchange between populations occupying highly curved and planar regions of the bicelle.27 Thus, its chemical shift reflects the proportion of these two populations of DHPC. Using the method of analysis formulated by Triba et al.,27 with the simplifying assumptions that both the 31P NMR isotropic and anisotropic chemical shifts of DMPC and DHPC are identical in the two environments and that DMPC never occupies highly curved regions, one may calculate an effective ratio of planar-to-curved phospholipid populations, q*, from the observed chemical shifts of DHPC and DMPC via eq 2

q* )

ω* ] [ 1q -+ ω*

(2)

where q ) DMPC/DHPC, as usual, and ω* ) ωDHPC/ωDMPC, where ωDHPC and ωDMPC are the observed chemical shifts of DHPC and DMPC, respectively. The results of this calculation

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Figure 3. Temperature-dependent 31P NMR spectra of (A) positively magnetically aligned bicelles composed of 100/5/1 (mol/mol/mol) DMPC/ DMPG/DMPE-PEG2000 + DHPC in the ratio q ) (DMPC + DMPG + DMPE-PEG2000)/DHPC ) 4.5 and (B) negatively magnetically aligned bicelles composed of 100/5 (mol/mol) DMPC/DMPG + DHPC in the ratio q ) 4.5. All samples contained 25% w/w lipid/water. The spectra were acquired at the temperature indicated in the figure. Positively magnetically aligned bicelles included ytterbium in the ratio Yb3+/P ) 1/75; negatively magnetically aligned bicelles did not. The various chemical shifts of the observed resonances are listed in Tables 3 and 4 for the spectra in (A) and (B), respectively. Table 3. 31P NMR Chemical Shifts as a Function of Temperature for Positively Magnetically Aligned Bicellesa chemical shift (ppm)b,c temp °C

DMPC

DHPC

q* ) (q + ω*)/ (1 - ω*)d

45 40 35 30 25

20.0 20.7 20.3 16.4 17.6

15.9 12.6 9.3 4.9 2.1

25.8 13.1 9.1 6.8 5.2

q ) 4.5, 100/5/1/23.5 (mol/mol/mol/mol) DMPC/DMPG/DMPEPEG2000/DHPC Yb3+/P ) 1/75, 25% w/w lipid/water. b Relative to 85% phosphoric acid. c DMPG and DMPE-PEG2000 resonances could not be resolved in the presence of Yb3+. d ω* ) ωDHPC/ωDMPC. a

are listed in Tables 1-4 and indicate that the equilibrium distribution of DHPC shifts away from curved and toward planar regions of the bicelle upon increasing either q or temperature. This is in essential agreement with, and confirms the findings of, Triba et al.27 and their mixed bicelle model. We will examine

Table 4. 31P NMR Chemical Shifts as a Function of Temperature for Negatively Magnetically Aligned Bicellesa chemical shift (ppm)b temp °C

DMPC

DMPG

DHPC

q* ) (q + ω*)/ (1 - ω*)c

40 35 30 25

-12.5 -12.1 -11.7 -11.7

-8.6 -8.2 -7.8 -7.7

-6.8 -5.0 -3.5 -2.7

11.1 8.4 6.8 6.2

a q ) 4.5, 100/5/23.3 (mol/mol/mol) DMPC/DMPG/DHPC, Yb3+/P ) 0, 25% w/w lipid/water. b Relative to 85% phosphoric acid. c ω* ) ωDHPC/ ωDMPC.

next the consequences of this shift in equilibrium DHPC distribution for water diffusion in such bicellar mixtures. As to the morphology of these bicelles, whether discoidal, or chiral nematic ribbons, or perforated lamellae, such 31P NMR do not distinguish readily between these possibilities. Nevertheless, the weight of evidence from a combination of techniques including

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Figure 4. 1H NMR spectra (35 °C) of positively magnetically aligned bicelles as a function of the field gradient pulse amplitude in the STE PFG NMR sequence. Bicelles were composed of 100/5/1 (mol/mol/mol) DMPC/DMPG/DMPE-PEG2000 + DHPC in the ratio q ) (DMPC + DMPG + DMPE-PEG2000)/DHPC ) 4.5 at 25% w/w lipid/water plus ytterbium in the ratio Yb3+/P ) 1/75. The gradient pulse amplitude varied progressively up to 244 G cm-1, with a gradient pulse duration of 5 ms, spin echo delay of 10 ms, and a stimulated echo delay of 100 ms. The water resonance at 4.7 ppm decays rapidly due to water’s fast diffusion.

SANS,19,20 polarized optical microscopy,22 cryo-EM,25 and diffusion NMR,34 indicates that when negatively charged amphiphiles such as DMPG or DMPE-PEG are present within the bicellar mixture, as they are in the mixtures examined here, the perforated lamellar morphology is preferred. In the following we will assume, therefore, the presence of perforated bicellar lamellae to interpret our water diffusion measurements and only latterly concern ourselves with the consequences for the case that this assumption is incorrect. General Features of STE PFG 1H NMR Spectra of Magnetically Aligned Bicelles. Figure 4 shows a series of 1H NMR spectra of Yb3+-doped q ) 4.5 bicelles at 35 °C as a function of gradient amplitude in the STE PFG NMR sequence. The intense resonance at 4.7 ppm is assigned to HDO. Other proton resonances, such as those arising from the bicellar lipids, are absent in such spectra due to their rapid transverse relaxation relative to the echo delays used in the STE PFG NMR sequence. In particular, the choline methyl resonances of DMPC and DHPC, which would appear in the vicinity of 3.8 ppm, are absent under these conditions, as are the ethylene oxide resonances of DMPE-PEG 2000. Note that in negatively magnetically aligned bicelles, i.e., in the absence of Yb3+, such resonances are visible. General Features of Water Diffusion in Bicelles from STE PFG 1H NMR Measurements. In Figure 4 it is evident that the intensity of the water resonance decays rapidly with increasing gradient amplitude, as expected given water’s small size. The echo amplitude depends on the experimental and sample variables as per eq 3

( ) ( )

I ) I0 exp

-2τ2 -τ1 exp exp[-D(γgδ)2(∆ - δ/3)] T2 T1

(3)

where δ (s) is the duration of the square gradient pulse of magnitude g (Tm-1), γ is the magnetogyric ratio, and ∆ ) τ1 + τ2 (s) is the experimental diffusion time, while T1 and T2 are the

longitudinal and transverse relaxation times, respectively. The isotropic diffusion coefficient is obtained from the slope in a plot of Ln(I/I0) versus k ) [(γgδ)2(∆ - δ/3)]. Experimentally, either the gradient pulse amplitude, or its duration, or the diffusion time, is incremented progressively. In the STE PFG NMR sequence the diffusion time ∆ is limited by T1 rather than T2, which confers the ability to employ longer diffusion times, thereby facilitating diffusion measurements for cases of slower diffusion, or lower gradient strengths, or lower γ nuclei.36 Figure 5 compares the diffusive intensity decays for bulk water versus water within either positively or negatively magnetically aligned q ) 4.5 bicelles, all at 35 °C. One observes that the intensity decays are virtually linear in all three cases, indicating that a single effective average diffusion coefficient describes the water diffusion in each situation. Furthermore, there was no diffusion time dependence of the diffusion coefficient over a range of diffusion times 110 ms e ∆ e 610 ms. Hence, only ∆ ) 110 ms results are considered further. For the case of a diffusant confined between the lamellae of magnetically aligned bicelles, the diffusion coefficient is anisotropic and may be represented in terms of a second-order symmetric diffusion tensor. In the molecular frame defined with respect to the perforated parallel plate geometry in Figure 1, only two independent diffusion tensor elements persist: specifically, D| and D⊥, representing, respectively, diffusion parallel and perpendicular to the bilayer normal direction.40,41 When, as in our case, the pulsed field gradients are applied solely along the laboratory z-direction (defined by the direction of the principal magnetic field B0), the g2D term in eq 3 is replaced by gz2Dzz, where Dzz is the particular element of the symmetric Cartesian diffusion tensor, as defined in the laboratory frame, which is measured under such circumstances. Transforming from the (40) Callaghan, P. T.; So¨derman, O. J. Phys. Chem. 1983, 87, 1737–1744. (41) Lindblom, G.; Ora¨dd, G. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 483–515.

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Figure 5. Diffusive intensity decays from STE PFG NMR spectra (35 °C) of bulk water (inverted triangles), negatively magnetically aligned bicelles (open circles), and positively magnetically aligned bicelles (closed circles). Positively magnetically aligned bicelles were composed of 100/ 5/1 (mol/mol/mol) DMPC/DMPG/DMPE-PEG2000 + DHPC in the ratio q ) (DMPC + DMPG + DMPE-PEG2000)/DHPC ) 4.5 at 25% w/w lipid/water plus ytterbium in the ratio Yb3+/P ) 1/75. Negatively magnetically aligned bicelles were composed of 100/5 (mol/mol) DMPC/ DMPG + DHPC in the ratio q ) 4.5. Solid lines are the fits of eq 3 for the case ∆ ) 110 ms, δ ) 5 ms, and the calibrated maximum gradient strength (3.44 Tm-1). The particular diffusion coefficient is obtained from the slope and corresponds to D0 ) 2.44 × 10-9 m2 s-1 for bulk water, D⊥ ) 2.1 × 10-9 m2 s-1 for negatively magnetically aligned bicelles, and D| ) 9.85 × 10-10 m2 s-1 for positively magnetically aligned bicelles.

molecular frame to the laboratory frame yields the relationship between the apparent diffusion coefficient measured in the laboratory frame Dzz and the diffusion tensor elements in the relevant molecular frame, as per eq 4

Dzz ) D⊥ sin2 θ + D| cos2 θ

(4)

where θ is the polar angle between the bilayer normal and the applied field gradient. Thus, for negatively magnetically aligned bicelles, where the bilayer normal is oriented preferentially at 90° relative to the magnetic field direction, when the field gradients are applied exclusively along the laboratory z-direction the STE PFG NMR experiment directly measures D⊥, corresponding to diffusion along the direction of the slit channel between adjacent bicelles, referred to hereafter as the longitudinal direction. Similarly, for positively magnetically aligned bicelles, where the bilayer normal is oriented uniformly at 0° relative to the magnetic field direction, when the field gradients are applied exclusively along the laboratory z-direction the STE PFG NMR experiment directly measures D|, corresponding to diffusion across the slit channel between adjacent bicelles, referred to hereafter as the transverse direction. As the slopes in Figure 5 show, the longitudinal water diffusion coefficient D⊥ is reduced to about 85% of that of bulk water under otherwise identical conditions. This effect is attributed to slowly diffusing interfacial water interacting with the lipid headgroup region but in fast exchange with bulk water not affected by the lipid head groups, rather than to any specific effect of confinement to the slit channel, since a water molecule is quite small relative to the transverse dimensions of the slit channel. Otherwise, water diffusion is unrestricted in this direction over a length scale corresponding to the root-mean-square (rms) displacement, 〈x2〉1/2 ) (2D∆)1/2. For this particular diffusion coefficient (D⊥ ) 2.1 × 10-9 m2 s-1) at this particular diffusion

time (∆ ) 110 ms) the rms water displacement equals roughly 20 µm. This corresponds to the size of an individual bicelle domain within the mosaic of domains of which a bicelle sample is composed.4,21,22 Figure 5 also shows that the transverse water diffusion coefficient D| is reduced to 9.8 × 10-10 m2 s-1, i.e., only 40% of that of bulk water at the same temperature. Clearly the bicelles significantly obstruct water diffusion in the transverse direction. Nevertheless, this diffusion coefficient is still far larger than that at the lamellar limit, estimated to lie in the range between D, 10-13 and 10-14 m2 s-1.42 For example, in carefully annealed macroscopically oriented lipid bilayers held between glass plates, the water diffusion coefficient in the transverse direction fell below the lower limit of approximately 4 × 10-12 m2 s-1 capable of being detected with the available gradient strength.43 Thus, in comparison to such highly lamellar lipid bilayer sheets, our positively magnetically aligned bicelles are riddled with defects allowing ready water passage in the transverse direction. We construe that such defects arise from the presence of DHPC and the consequent formation of toroidal perforations within the lamellae. The rms diffusional displacement calculated for this diffusion coefficient (D| ) 9.8 × 10-10 m2 s-1) and diffusion time (∆ ) 110 ms) equals roughly 10 µm. Given that the lamellar repeat spacing in bicelles of similar composition and water content has been measured to be 100 Å,21,22 it follows that water diffusing in the transverse direction in these experiments has crossed roughly a thousand individual lamellar layers. Thus, we are measuring here an average behavior over many repeats. Specific Dependence of Water Diffusion in Bicelles on q Ratio and Temperature. Figure 6A illustrates the manner in which the water diffusion coefficient varies with q for both positively and negatively magnetically aligned bicelles at 35 °C. In all cases diffusion in the longitudinal direction (D⊥) is several times faster than diffusion in the transverse direction (D|), demonstrating again that the bicellar lamellae act to differentially obstruct water diffusion in the transverse direction. One predicts that, if such diffusion occurs primarily through lamellar defects, or perforations, formed by DHPC, then transverse diffusion (D|) will scale inversely with q, and indeed this is observed to be the case. On the other hand, diffusion along the longitudinal channel axis (D⊥) should be virtually independent of q, a prediction which is not born out by experiment. However, the decreased longitudinal water diffusion coefficient at higher q for the negatively magnetically aligned bicelles can be attributed directly to the poorer quality of magnetic alignment achieved in these cases, as evident in the 31P NMR spectra in Figure 2B. In fact, such a decrease in diffusion is the behavior expected from eq 4 for an elliptical distribution of bicelle alignments about θ ) 90° given D⊥ > D|. Figure 6B illustrates the manner in which the water diffusion coefficient varies with temperature for both positively and negatively magnetically aligned bicelles having q ) 4.5. The temperature dependence of the diffusion coefficient of bulk water is shown as well for reference purposes. Again, in all cases diffusion in the direction along the longitudinal channel axis (D⊥) is several times faster than diffusion in the direction across the slit channel long axis (D|). Both the bulk water diffusion and the water diffusion along the longitudinal channel axis (D⊥) increase with increasing temperature as expected. However, counterintuitively, water diffusion transverse to the slit channel long axis (D|) actually decreases with increasing temperature. This unanticipated temperature dependence of D| is in fact also consistent with the notion that water diffusion in

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Figure 6. (A) Water diffusion coefficients from STE PFG NMR diffusion measurements on magnetically aligned bicelles as a function of q ) (long-chain amphiphiles)/DHPC: negatively magnetically aligned bicelles (open circles); positively magnetically aligned bicelles (closed circles). The solid lines are meant to guide the eye. (B) Water diffusion coefficient from STE PFG NMR diffusion measurements on magnetically aligned bicelles as a function of temperature. In each case q ) (long-chain amphiphiles)/DHPC ) 4.5: bulk water (inverted triangles); negatively magnetically aligned bicelles (open circles); positively magnetically aligned bicelles (closed circles). The solid lines are meant to guide the eye.

the transverse direction occurs principally through the defects/ perforations formed by DHPC. As shown by the data in Table 3, q* increases with increasing temperature, meaning that the amount of DHPC resident in such perforations, and hence the number of such perforations, likewise decreases. Studies of water permeation across single lipid bilayer membranes containing cylindrical pores have established that, for the case of pore radii large relative to the size of a water molecule, a continuum model is appropriate wherein the principal determinant of transbilayer water permeation is simply the fractional surface area of pores.42 The planar regions of the bicelles act, therefore, to obstruct transverse water diffusion. In the presence of multiple sequential obstructions, such as the multiple bicelle lamellar repeats traversed by the water in our diffusion measurements, obstructed diffusion models indicate that diffusion decreases as the volume fraction of obstructions f increases and will cease upon reaching the volume fraction percolation threshold f*.44 In our case of multiple bicelle lamellar repeats uniformly aligned with respect to one another, the relevant volume fraction

is that of the lamellar bicelle region relative to the pore region, and the percolation threshold is reached only when the volume fraction of pores approaches zero. Since it is reasonable to assume that lamellar and pore regions have identical transverse dimensions, the case reduces to that of the area fraction of lamellar surface to that of pore surface, identical to the case of permeation across a single lipid bilayer. This suggests the following simple relationship between the reduced transverse water diffusion coefficient and the effective ratio of planar- versus perforationresident DHPC, q*,

D| ) D0

1 1 ) Alam 1 + Bq* 1+ Aperf

(5)

where D0 is the corresponding diffusion coefficient of bulk water, while Alam and Aperf are the respective surface areas of lamellar regions and perforations. (We ignore in eq 5 hydration effects which are equally potent at slowing D| and D⊥ but which, given

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[

a a2 B) π -2 2 k k

]

If instead, one assumes, as per Triba et al.,27 a hemielliptical DHPC coating, having eccentricity “a/b”, lining a toroidal pore of radius “k”, and assuming further that the number of DHPC per toroid is dictated by the relative volumes of the hemielliptical toroid versus that of DHPC, then

[

a 2 ab B) π - 2 k 3k

Figure 7. Reduced water diffusion coefficient D|/D0 in positively magnetically aligned bicelles as a function of the calculated surface fraction of pores in bicellar lamellae. The latter was calculated according to eq 5 using the diffusion coefficients shown in Figure 6 and the values of q* listed in Tables 1 and 3, assuming B ) 0.16 (see text). Open squares: q series at 35 °C. Closed circles: temperature series at q ) 4.5

the value of D⊥/D0, 0.86, appear to be of secondary concern.) B is a model-dependent constant of proportionality relating the number of DHPC occupying perforations to the fractional surface area of those perforations. Equation 5 indicates that the volume fraction of toroidal perforations within the bicellar lamellae φperf is directly equal to the reduced transverse diffusion coefficient, i.e., φperf ) Aperf/ (Aperf + Alam) ) D|/D0. Thus, for the case of q ) 3.5 bicelles at 35 °C we find D|/D0 ) 0.477 ) φperf. This is in good agreement with the volume fraction of toroidal perforations reported by Nieh et al.19 from SANS measurements on compositionally quite similar, albeit not identical, bicellar mixtures at 45 °C. In Figure 7 the reduced transverse diffusion coefficient is plotted as a function of 1/(1 + Bq*) for both the q-dependent and the temperature-dependent measurements in Figure 6, parts A and B, using the q* values listed in Tables 1 and 3. The solid line indicates the idealized 1:1 relationship between the reduced transverse diffusion coefficient and the fractional surface area of perforations. The fact that the q dependence and the temperature dependence of the transverse water diffusion coefficients fall on a common curve when treated in this fashion indicates that the common element is indeed the fraction of DHPC resident in perforations as derived assuming the mixed bicelle model. The value of B ) 0.16 for the line-of-fit in Figure 7 was chosen simply to yield the best 1:1 correspondence between the reduced transverse diffusion coefficients and the parameter 1/(1 + Bq*). B can be derived for any specific model of DHPCcoated toroidal perforations. For instance, Soong and Macdonald45 assumed a hemispherical DHPC coating, having radial dimension “a” lining a toroidal pore of radius “k”, and assumed further that the number of DHPC per toroid is dictated by the relative surface area of the hemispherical toroid versus that of DHPC, leading to (42) Finkelstein, A. Water MoVement through Lipid Bilayers, Pores, and Plasma Membranes. Theory and Reality; Wiley and Sons: New York, 1987. (43) Wa¨sterby, P.; Ora¨dd, G.; Lindblom, G. J. Magn. Reson. 2002, 157, 156– 159. (44) Mercier, J. F.; Slater, G. W. J. Chem. Phys. 2000, 113, 9109–9112. (45) Soong, R.; Macdonald, P. M. Biophys. J. 2005, 89, 1850–1860.

]

Taking a ) 20 Å, i.e., the width of a DMPC monolayer, and b ) 11 Å, i.e., the length of DHPC, yields a pore radius k ) 380-400 Å for both models for the case B ) 0.16. A particular concern with such geometric models as applied to diffusion in bicelles is that they treat the lamellar obstructions and the toroidal perforations as essentially static, passive structures. However, the 31P NMR results indicate that, on the contrary, the perforations must be highly dynamic, given that DHPC exchanges rapidly between planar and curved regions. Likewise, the size of the perforations may well fluctuate, which might actually assist transverse water diffusion in a manner akin to peristaltic pumping. Furthermore, the model assumes essentially complete obstruction of transverse water diffusion by the planar lamellar regions of the bicelles. However, the DHPC population residing within the planar region is likely to increase water permeation through that region, since DHPC is essentially a surfactant and many surfactants are known to enhance bilayer permeation, presumably through creation of transient holes.46-49 Since we observe an average diffusion, both pathways might potentially contribute, but their relative contribution is uncertain. Such uncertainties suggest that, for the purpose of estimating the size of the DHPC-rich toroidal perforations in bicelles, geometric models predicting the q* dependence of the reduced transverse water diffusion coefficient D|/D0 provide at best an absolute upper bound on the pore size. Indeed, the pore size deduced in this fashion is more than an order of magnitude larger than that obtained by Nieh et al.19 from their fitting of SANS data on similar bicellar mixtures, although these authors could not exclude the possible presence of much larger pores. Larger diffusants like PEG, however, should be far more sensitive to the details of the size of the perforations in diffusion experiments. Such diffusion measurements are underway and will be described elsewhere. PFG NMR diffusion measurements are not particularly sensitive to the shape of the lamellar defects. For instance, transverse water diffusion measurements in the lamellar phase of surfactant systems clearly demonstrated the presence of lamellar defects but could not unequivocally distinguish between different structural models for the defects.50 Moreover, in bicelle mixtures morphologies other than perforated lamellae are possible, although the weight of evidence in the literature supports our assumption that the perforated lamellar morphology is relevant for these bicellar mixtures under these conditions. Can these PFG NMR water diffusion measurements differentiate a defective lamellar from the discoidal bicelle morphology expected at low q and/or lipid concentration? In surfactant systems exhibiting discoidal geometries PFG NMR water diffusion anisotropy measurements, (46) Ruiz, J.; Gon˜i, F. M.; Alonso, A. Biochim. Biophys. Acta 1988, 937, 127–134. (47) Ueno, M. Biochemistry 1989, 28, 5631–5634. (48) Edwards, K.; Almgren, M. Langmuir 1992, 8, 824–832. (49) Nagawa, Y.; Regan, S. L. J. Am. Chem. Soc. 1992, 114, 1668–1672. (50) Holmes, M. C.; Sotta, P.; Hendrikx, Y.; Deloche, B. J. Phys. II 1993, 3, 1735–1746.

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in combination with stochastic simulations of combined obstruction and hydration effects via an “equivalent cell approximation” (ECA), were shown to be sensitive to the dimensions of the surfactant discoidal self-assemblies.51,52 The characteristic parameters in such measurements are the reduced transverse and longitudinal diffusion coefficients A| ) D|/D0 and A⊥ ) D⊥/D0, the isotropic average reduced diffusion coefficient 〈A〉 ) 1/3(A| + 2A⊥) and the diffusional anisotropy R ) (A| - A⊥)/〈A〉.The experimental value of the latter is scaled by the orientational order of the surfactant self-assemblies, such that Rexp ) SRtheory. Halle and co-workers51,52 present expressions whereby such obstruction factors may be interpreted in terms of the aspect ratios of oblate, or prolate, or discoidal, surfactant self-assemblies, as a function of the volume fraction of obstructions. The use of the example of q ) 4.5 bicelles at 35 °C, where D| ) 9.85 × 10-10 m2 s-1, D⊥ ) 2.10 × 10-9 m2 s-1, and D0 ) 2.44 × 10-9 m2 s-1, yields A| ) 0.403, A⊥ ) 0.858, and 〈A〉 ) 0.709, while Rexp ) -0.641 and Rtheory ) -0.96. To put these values in perspective, in the limit of defect-free lamellae, with no hydration considerations, D| ) 0 and D⊥ ) D0, such that Rtheory ) -3/2. Applying these values to the expressions of Halle and co-workers51,52 for the case of discoidal obstructions at a volume fraction of 0.25 yields an apparent aspect ratio of F ) 6.4. Specifically including considerations of hydration effects would yield an even smaller apparent aspect ratio. Compare this result with that calculated using the formula of Vold and Prosser26 for a discoidal bicelle having aspect ratio F ) R/r, where R is the long semiaxis (i.e., the disk radius) and r the short semiaxis (i.e., half the bilayer thickness). For an “ideal” bicelle, i.e., wherein the DHPC is confined to edge regions, the case q ) 4.5 yields F ) 15, whereas for the “mixed” bicelle, i.e., wherein DHPC is distributed between edge and planar regions, the corresponding case q* ) 9.2 at 35 °C yields F ) 30. Note further, that theoretical,53,54 computational,55,56 and experimental (51) Jo´hannesson, H.; Halle, B. J. Chem. Phys. 1996, 104, 6807–6817. (52) Jo´hannesson, H.; Furo´, I.; Halle, B. Phys. ReV. E 1996, 53, 4904–4917. (53) Onsager, L. Ann. N.Y. Acad. Sci. 1949, 51, 627–659.

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studies57 agree that aspect ratios greater than 10 seem to be required in order to obtain a nematic ordered phase for discoidal objects at this volume fraction. Thus, the apparent aspect ratio obtained from comparing our water diffusion anisotropy measurements with theoretical obstruction effects for discoidal obstructions seems unreasonably small. This may be due in part to the fact that such theories treat the self-assemblies as hard, essentially static, obstructions, with hydration effects due to water binding at the surface, when they are, instead, rather dynamic at the molecular level.

Conclusions The mixed bicelle model posits that in bicelles the short-chain lipid DHPC exists in fast exchange between regions of high curvature and regions of high planarity. PFG NMR measurements of water diffusion in positively magnetically aligned bicelles as a function of q and temperature demonstrate that obstruction of transbicellar water diffusion is directly proportional to the fraction of DHPC resident in edge versus planar bicelle regions, determined from 31P NMR spectral analysis, as opposed to merely the global DHPC content. This observation directly supports the mixed bicelle model. Although water diffusion measurements permit an upper bound to be placed on the size of the DHPC-rich toroidal perforations in the bicellar lamellae, further studies involving larger diffusants are necessary to better define their dimensions. Acknowledgment. This research was supported by operating and equipment Grants from the Natural Science and Engineering Research Council (NSERC) of Canada. LA801739A (54) Forsyth, P. A., Jr.; Marcˇelja, S.; Mitchell, D. J.; Ninham, B. W. AdV. Colloid Interface Sci. 1978, 9, 37–60. (55) Forsyth, P. A., Jr.; Marcˇelja, S.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans 2 1977, 73, 84–88. (56) Veerman, J. A. C.; Frenkel, D. Phys. ReV. A 1992, 45, 5632–5648. (57) Miyamoto, N.; Nakato, T. J. Phys. Chem. B 2004, 108, 6152–6159.