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J. Phys. Chem. 1993,97,2952-2957
Estimating Lipid Lateral Diffusion in Phospholipid Vesicles from 13C Spin-Spin Relaxation Jeffrey F. Ellena, Leslie S. Lepore, and David S. Cafiso' Department of Chemistry and Biophysics Program, University of Virginia, Charlottesville, Virginia 22901 Received: October I, 1992; In Final Form: January 19, I993
Carbon 13 spin-spin relaxation rates (T2-') were measured in both sonicated and extruded lipid vesicle preparations and were analyzed using several Lorentzian spectral density functions. A minimal spectral density function that includes the effects of internal acyl chain motions, axial rotation, and phospholipid wobble can accurately account for the spin-lattice relaxation rates (TI-l) and 13C-lH nuclear Overhauser effects in these vesicle preparations. Not surprisingly, this spectral density function cannot account for the I3C 7'2-l values, which should be strongly influenced by slower molecular motions. When this spectral density function is extended to include motions due to lipid lateral diffusion and vesicle tumbling, the experimental T2-1 values can be accurately reproduced. However, the lateral diffusion coefficient required to fit the values of T2-1 is larger by almost 2 orders of magnitude than values usually found for membrane phospholipids. By modifying the spectral density function to include an additional motion between 1 W and s the value of D required to fit the T2-l data can be lowered; however, if lo-' cm2/s is taken as a reasonable value for D,any additional motion must be virtually isotropic in order to account for the spin-spin relaxation data. There are a number of sources of motion in this time scale, but none are likely to produce a large-amplitude, isotropic motion in small lipid vesicles. The simplest explanation for the 13CT2-l data is that lateral diffusion rates are slightly faster in lipid vesicles (by a factor of 5-10) than in planar or multilamellar systems.
Introductioo The physical chemistry of the phospholipid bilayer is critical for the behavior and function of biological membranes. In particular, the liquid crystalline properties of the phospholipid bilayer and the lateral mobility of membrane components mediate a number of fundamental and interesting biological processes. The rapid lateral diffusion of lipids was established over two decades and processes such as intracellular signaling and electron transport are now known to be mediated by the lateral membrane diffusion of proteins and small lipid soluble molecules. Clearly, the lateral diffusion rate of phospholipids is an intrinsic membrane property that is important to measure, because it provides information on the rates of these biological processes. In addition, the lipid diffusion rate will be strongly affected by the strength of interactionsamong lipid molecules in bilayers and thus provides information of these molecular interaction^.^ Processes such as the phase separation of lipid components will affect lipid diffusion rates, and a measure of the diffusion rate can provide information on the size and shape of lipid domain^.^ Many spectroscopic measurements in bilayers (for example magnetic resonances measurements) are also stronglyinfluenced by lateral diffusion, and accurate diffusion coefficients are necessary for a correct interpretation of the data. For these reasons, a large number of measurements have been carried out to determine the lateral diffusion rate of lipids. Techniques such fluorescence photobleaching, pulsed field gradient NMR,and EPR imaging yield lateral diffusion coefficients in the liquid crystalline state on the order of 10-8-10-7 cm2S-I.~.~ These measurements examine the diffusion process over long, macroscopic distances. Measurements using fluorescence and magneticresonance probes examine diffusion over shorter distance scales and generally yield slightly larger diffusion rates of around IO-' cm2 s-I. These measurements include a fluorescence measurement based on eximer formation and EPR techniques based on Heisenberg spin-exchange and/or electron-electron dipole interactions.Gs Many of these measurements are model dependent and open to interpretation; for example, extracting a All correspondenceshould beaddrcssed to this authorat the Department of Chemistry.
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diffusion coefficient from eximer formationdepends heavily upon an accurate value for the length of a single diffusion step, a value that is difficult to obtain. Quasielastic neutron scattering is an approach that has recently been used to estimate lipid lateral diffusion rates. This technique yields local in-plane and outof-plane diffusional motions that are quite fast but yields lateral diffusion rates of about c ~ ~ / s . ~ NMR spectroscopy provides a powerful approach to study dynamics, because molecular motions provide the time varying local magnetic fields that promote nuclear relaxation. In membranes, the application of NMR relaxation to study dynamics has been challenging. The inherent complexity of motion in the lipid bilayer makes thedevelopmentof realistic models todescribe the lipid motion difficult. Nonetheless, NMR has played a major role in elucidatingthe molecular dynamics of these systems. Spinlattice relaxation (TI) in lipid vesicle systems appears to be reasonably well described by a minimal model shown in Figure 1.l0 In this model, a motion associated with internal chain dynamics and lipid rotation is described by a fast correlation time 7j and an associated order parameter 27,. The correlation time 7t and the order parameter St describe a slower motion due to phospholipid tilt. A spectral density function derived from these motions reproduces a wide range of TI relaxation data as wellas IH-l3Cnuclear Overhauser effects (NOES) in bilayers.lOJ1 In lipid vesicles, the rotation of the vesicle and phospholipid diffusion combine to produce an isotropic motion in the microsecond time scale. However, this motion is too slow to contribute to TIrelaxationat higher Larmor frequencies.'l Similarly,other slow motions such as order director fluctuations3do not contribute to spin-lattice relaxation in vesicles at higher Larmor frequencies. Spin-spin relaxation has not been extensively studied in lipid vesicles systems; in fact, only one estimate of l3C spin-spin relaxation in vesicles (obtained from line-width measurements) has been reported.I2 Spin-spin relaxation rates should be particularly useful, because they will be sensitive to the slower molecular motions described above. In vesicles, I3C T2 rates are expected to be strongly influenced by lipid lateral diffusion and vesicle tumbling. Order director fluctuations and vesicle shape changes should have relatively low amplitudes in small lipid vesicles and are not expected to make large contributions to the Q 1993 American Chemical Society
Translational Diffusion in Lipid Vesicles
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2953 measure relaxation processes has dramatically improved. Although not yet completely understood, a wide range of NMR relaxation data can be well accounted for by a relatively simple model for molecular motion. A minimal spectral density function based on this model was given by Pastor et al.Io and is listed in eq 1. It is similar to functions described by Bocian and Chant*
Figure 1. A diagram illustrating the most important motions that contribute to 'ICrelaxation in lipid bilayers. T, is a short correlation time that describes local bond isomerizations, torsions, librations, as well as axial lipid rotation. iIis a longer correlation time that describes phospholipid wobble or tilt. S, and S, are the order parameters associated with these motions. T" describes the isotropic reorientation of the lipid molecule in the vesicle as a result of vesicle rotation and lipid diffusion. T, and T~ make the most important contributions to spin-lattice relaxation and 'H-I3C NOES.'I Slower motions, such as those described by T,, are expected to strongly influence 'ICspin-spin relaxation.
spin-spin relaxation rate. By including motions due to vesicle rotation and lateral diffusion, it should be possible to account for the measured values of T2-I. In principle, the spin-spin relaxation rate, when combined with an analysis of the high-frequency motions from T Iand NOE data, should also allow for an estimate of the lateral diffusion of lipids in vesicles. In this report, we describe the measurement of I3C spin-spin relaxation rates in lipid vesicle systems and we analyze the data by extending the spectral density function to include molecular motions that w u r on slower time scales. This analysis shows that the T2rates can be accurately accounted for by this extended model; however, the lateral diffusion rates that are obtained are much larger than expected. Additional motions of the lipid that may makecontributionsto the T2ratesareincludedin theanalysis. These motions alone cannot account for the Tz-1data, and the simplestinterpretation of the data is that lateral diffusionis slightly faster in small lipid vesicles than in planar and multilamellar systems.
and by B r o ~ n , l ~ , ~it~iscapableof and fitting spin-lattice relaxation data collected at Larmor frequencies between 10 and 500 MHz. Two correlation times T, and T , described the motion of methylene or methine groups and are illustrated in Figure 1. The first, T,, is a relatively short correlation time that describes local motions due to bond isomerizations, torsions, librations, and rotation of the phospholipid molecule about its long axis. These motions are in the fast motional limit; that is, ( w T ~ 10 MH2).19920342However, recent work indicates that ODFs make significant contributions to the total membrane spectral density only at Larmor frequencies < I MHz.3J0.43-48 In fact, the recent work of Halle' indicates that the ODFs do not contribute to spin relaxation in bilayer vesicles with diameters
