Translational Dynamics of Water at the Phospholipid Interface

Article pubs.acs.org/JPCB

Translational Dynamics of Water at the Phospholipid Interface Ken G. Victor,† Jean-Pierre Korb,‡ and Robert G. Bryant*,† †

Chemistry Department, University of Virginia Charlottesville, Virginia, United States Physique de la Matière Condensée, Ecole Polytechnique, CNRS, 91128, Palaiseau, France

‡

ABSTRACT: The residual water-proton magnetic relaxation dispersion profile obtained from suspensions of phospholipid vesicles in deuterium oxide was found to be a logarithmic function of the proton Larmor frequency at high magnetic field strengths, and independent of Larmor frequency at low magnetic field strengths. The residual proton relaxation is caused by dipole−dipole coupling between the residual water proton in otherwise deuterated water and the phospholipid protons. The logarithmic dependence on magnetic field strength is the signature of water-proton diffusive exploration on the interface that is approximately two-dimensionally constrained. Application of relaxation theory for two-dimensional diffusion to the spin−lattice relaxation data yields a translational correlation time of approximately 70 ps for water diffusing in the interface of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) vesicles.

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the magnetic field strength for 1-palmitoyl-2-oleoyl-sn-glycero3-phosphocholine (POPC) vesicles suspended in deuterium oxide. We observe the residual protons in the solvent; the 1 HOD concentration is of the order 200−300 mM in protons, and the H2O concentration is negligible. Because the H−D dipolar coupling is weak, the residual HOD proton relaxation is dominated by the transient intermolecular dipolar couplings between the water proton and the phospholipid protons. These intermolecular couplings are modulated by the relative translational diffusion of the interacting protons, and because the proton−proton dipolar coupling strength falls rapidly with distance, the water-proton relaxation is most strongly influenced by the nearest neighbor protons when the water contacts the phospholipid. However, the water two-dimensional diffusion evidenced here enhances the reencounter probability dramatically between water and phospholipid protons and maintains the dipolar correlations that account for the logarithmic dependence of the spin−lattice relaxation rate constant on the magnetic field strength.

INTRODUCTION Translational diffusion of small molecules, including solvent, at a macromolecular interface may be biased by the excluded volume created by the macromolecule. For a protein solution, the proton spin−lattice relaxation rate was shown to be a logarithmic function of the magnetic field strength at high field strengths, which is consistent with a diffusional exploration of the interface that is geometrically biased and approximately two-dimensional.1 A phospholipid vesicle is a much larger object, and the intrinsic dynamics of the lipid assembly is significantly different from that of a protein or an inorganic surface. Phospholipids are critical components of living cells, and the dynamic parameters of the aqueous interface are an important aspect of their characterization and possibly function. Understanding water dynamics at the lipid interface is also helpful in the context of magnetic imaging and contrast control. Water diffusion in the vicinity of phospholipid vesicle surfaces has been previously investigated using paramagnetic contributions to the water-proton spin−lattice relaxation rate, and it was found that the apparent translational diffusion constant was reduced from that of the bulk by a factor the order of 3.2 The electron−nuclear coupling is relatively long-range, and the measurement integrates over all intermoment distances, i.e., all distances between the surface localized paramagnetic label and the large population of diffusing water-molecule protons. Although this measurement based on translational diffusion in the vicinity of a paramagnet is strongly weighted by the water protons closest to the paramagnet, the relaxation contributions from the strong electron−nuclear dipolar coupling include contributions from diffusing water spins several water diameters away from the interface. Thus, this characterization is not strictly representative of the water in intimate contact with the phospholipid interface. We report here an approach that localizes the water diffusion at the interface more strongly. We measure the proton spin−lattice relaxation rates as a function of © 2013 American Chemical Society

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EXPERIMENTAL SECTION The nuclear spin−lattice relaxation rate constants reported here were measured as a function of the magnetic field strength using an NMR spectrometer assembled in this laboratory and described previously.3,4 The spectrometer employs two magnetically isolated independent magnets separated by 82 cm. The high field magnet was constructed by Magnex Scientific, Co. (Oxford, U.K.), and provides a high resolution magnetic field of 7.05 T. The second magnet, positioned below the superconducting magnet in an iron shield, is a variable gap, Received: July 18, 2013 Revised: September 20, 2013 Published: September 23, 2013 12475

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iron core 4-in. electromagnet made by GMW (GMW Associates, San Carlos, CA). The magnetization decay measured as a function of the residence time in the satellite relaxation field is characterized by the spin−lattice time constant, T1, appropriate to the value of the satellite relaxation field. The magnetic relaxation dispersion profile is obtained by varying satellite field strength over the range of proton Larmor frequencies from 0.01 to 70 MHz. The relaxation rate constant of the 300 MHz superconducting polarization/detection field provides the high field limit. Data acquisition and sample movement are controlled by a Tecmag Apollo system which drives a NVS 4214 double solenoid air valve (SMC Pneumatics) used to direct pressurized air and vacuum that moves the sample between the two magnet systems. The NMR probe built in this laboratory includes a standard LRC single resonance circuit with an unload Q of approximately 150. The high field is typically shimmed to a 1H line width of 10 Hz or better which is stable throughout the impacts imparted by the sample excursions during measurement acquisitions. All experiments were conducted at ambient temperature of the driving gas supply, which was approximately 293 K. The residual water-proton peak is shifted 2−4 ppm to low field from the lipid protons, and relaxation dispersion of only the water peak was measured. The phospholipid vesicles were prepared from 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC) obtained from Avanti Polar Lipids (Alabaster, AL) and used without further purification. The desired mass of POPC was dissolved in chloroform and placed overnight in a vacuum desiccator to remove the organic solvent fully. The resulting lipid film was then hydrated by the addition of a buffer containing 100 mM KCl, 10 mM phosphate, pH 7.0, prepared in D2O. Using liquid nitrogen, unilamellar vesicles were produced by a well documented method5 consisting of five freeze−thaw cycles of this lipid suspension followed by 20 cycles of extrusion of the mixture through 1000 Å polycarbonate filters (Poretics, Livermore, CA) using a LiposoFast extruder (Avestine, Ottawa, Canada). Samples were thoroughly degassed in using a stream of nitrogen gas on the liquid surface contained in a nitrogen atmosphere. The absence of oxygen is verified by the very long T1 of the residual water protons, of order 20 s, and the absence of an oxygen induced relaxation dispersion.

Figure 1. The residual water-proton spin−lattice relaxation rate constant as a function of the applied magnetic field strength (represented in terms of the proton Larmor frequency) for a 40 mM suspension of POPC in D2O at ambient laboratory temperature. The parameters of eq 1 are A = 1 × 107 s−2, τdiff = 71 ps, τI = 6 μs, and 1/To1 = 0.03 s−1.

dispersion.6,7 Because the observed HOD relaxation dispersion is different from that reported by the lipid protons, the cross relaxation or magnetization transfer between the rare residual water protons and the pure lipid protons at the interface is weak and does not dominate the field dependence of the waterproton spin−lattice relaxation rates. The high field region of the relaxation dispersion has a logarithmic dependence on magnetic field strength that is characteristic of relaxation caused by diffusive exploration of a two-dimensional space.8−10 The phospholipid surface, of course, is remarkably dynamic on the time scales of the relaxation times measured or the reciprocal of the Larmor frequencies utilized here; thus, the measurement integrates over these short time fluctuations. There are no significant binding interactions to hold water at the lipid interface; if there were, we would observe a more Lorentzian-like dispersion curve with an effective midpoint reporting either an exchange lifetime or a global rotational correlation time for the vesicles. Neither is observed, as shown by the representative data of Figure 1. Nevertheless, the presence of the lipid occupies space that may not be simultaneously occupied by water, which biases the diffusive exploration by the freely diffusing water molecules. Proton NMR relaxation is a stimulated phenomenon driven by the coupling of the proton spins to the magnetic noise induced by molecular motions (translation, rotation, exchange, etc.). Varying the magnetic field (NMRD) changes the proton angular Larmor frequency ωI, and thus explores the frequency dependence of the magnetic fluctuations (noise) to which the longitudinal nuclear spin relaxation 1/T1 is sensitive. This experiment provides a good test of theories that relate the measurement to the microdynamical behavior of a fluid even when it is in a complex environment such as a phospholipid membrane interface that may force more frequent reencounters of moving water proton-spin with proton-surface groups. From the first principles of relative translational diffusion in close proximity to a relatively immobile surface (not necessarily solid), the surface alters the time dependence of the probability of reencounters P(τ) inversely proportional to the volume V(τ) explored by the water diffusion. The time dependence of V(τ) is directly related to the mean-square displacement, V(τ) ∝ ⟨r2(τ)⟩d/2, where d is the local Euclidean dimensionality, and at long times, ⟨r2(τ)⟩ ∝ τ. These scaling arguments thus relate the

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RESULTS AND DISCUSSION The spin−lattice relaxation rate constant for the rare residual HOD protons in D2O is shown as a function of magnetic field strength in Figure 1. The rate constants are significantly smaller than in H2O because both the intra- and intermolecular water− water dipolar interactions have been substantially reduced. The proton−deuteron dipolar coupling will make a relaxation rate contribution less than 0.02 s−1 because the deuteron moment enters the relaxation equation as the square and is approximately 6 times smaller than the proton moment. 1 HOD relaxation modulated by relative translational diffusion is weak because the proton concentration is smaller than that in water by approximately a factor of 400 and the process is second order. Further, the dispersion from this three-dimensional diffusion would not have the shape of that observed in Figure 1. Although the proton relaxation rate constant may become independent of magnetic field at small field strengths, it is linear in the logarithm of the Larmor frequency at high values over a remarkable range. These results are quite different from the magnetic field dependence of lipid-proton relaxation 12476

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time dependence of the reencounter probability, P(τ) ∝ 1/τd/2, to the local Euclidean dimensionality d. From the basic semiclassical treatment of the proton magnetic relaxation, the longitudinal relaxation rate 1/T1 is proportional to the spectral density which is given by a Fourier transform of the pairwise dipolar correlation function G(τ). Providing that the distances explored by the water diffusion (⟨r2(τ)⟩1/2 ≈ a few nm) close to a surface relaxation center stay small compared to the length of diffusion (≈(Dτ)1/2 ≈ a few μm), one finally finds that the frequency dependence of 1/T1, at least at low frequency ωI, depends strongly on the local dimensionality d. For instance, one has a logarithmic dependence when d = 2 and a power law (∝1/(ωI)1/2) when d = 1. Because the high field region of the relaxation dispersion has a logarithmic dependence on magnetic field strength (see Figure 1), one concludes that the relaxation is caused by diffusive exploration of a two-dimensional space.8−10 For three-dimensional diffusion, 1/T1 ∝ a − b(ωI)1/2, where a and b are constant. Thus, 1/T1 is constant at low frequency until the Larmor frequency is of the order of the reciprocal of the translational correlation time. Thus, one may safely rule out this possibility for the case studied here. The relaxation equation appropriate to the two-dimensional intermolecular spin dynamics in the immediate proximity of an interface is11 ⎧ ⎡ ⎪ ⎪ ⎢ 1 1 = o + Aτdiff ⎨ln⎢ T1 T1 ⎪ ⎢ ⎪ ⎢⎣ ⎩ ⎡ ⎢ + 4 ln⎢ ⎢ ⎢⎣

⎤ ⎥ 1 + ω τdiff ⎥ 2 τdiff 2 2⎥ + ω τdiff ⎥ τI ⎦ 2

2

( )

⎤⎫ ⎥⎪ ⎪ 1 + 4ω τdiff ⎥⎬ 2 τdiff + 4ω 2τdiff 2 ⎥⎥⎪ τI ⎦⎪ ⎭ 2

( )

provide a residual rate of 0.030−0.035, when oxygen is rigorously excluded. This value is almost twice what is expected from the proton−deuteron heteronuclear relaxation contribution. For this range of To1, the corresponding range of the water translational correlation time is from 78 to 71 ps. In spite of the uncertainty in the translational correlation time, it differs fundamentally from that measured from nitroxide spin-labeled phospholipids reported earlier.2 Because the field dependence for these paramagnetic cases was not logarithmic, a threedimensional model12−16 was used to interpret the data and yielded a translational correlation time for the interface that was 3−4 times slower than bulk water. In contrast, the logarithmic field dependence implies a two-dimensional translational model and the much weaker dipolar coupling localizes more strongly the depth of the interfacial region that drives the spin relaxation. Thus, a longer correlation time is expected. Using the standard relation for the diffusion constant D = l2/4τ with 3 Å for the size of the jump length and 71 ps for the translational correlation time gives D = 3 × 10−10 m2 s−1, which is an order of magnitude smaller than bulk water. The observation that the water-proton relaxation rate constants caused by the water protons coupling to the lipid protons is very small, in fact smaller than the water−water proton dipolar contributions in pure water, strongly supports the conclusion that pure lipid interactions make a negligible contribution to water-proton spin−lattice relaxation in tissue systems or phospholipid systems containing membrane-bound proteins or carbohydrates. Thus, the relaxation contribution from lipid based components in tissues is instead dominated by the macromolecular assemblies that are embedded in the lipid, including proteins and carbohydrates.17,18 These experiments show that the water diffusion within the intimate interface with the phospholipid surface is strongly influenced by the excluded volume provided by the dynamic lipid molecules and head groups. The resulting report through the magnetic field dependence of the water-proton spin−lattice relaxation rate is logarithmic over a wide range of Larmor frequencies, which implies that the diffusivity sensed by the magnetic relaxation experiment is effectively two-dimensional. There is a low-frequency cutoff consistent with exchange from the water from the interface region; however, the long surface lifetimes imply that the measurement is dominated by residual multilamellar vesicle structures in spite of the preparation protocol which is generally shown to yield unilamellar vesicles. The result that the water in the contact region defined in this case by the rapid decay of proton−proton magnetic dipole− dipole coupling with distance is approximately 10 times slower than the bulk liquid implies that solutes explore the contact region of the interface even more slowly, which significantly alters the time scales for diffusion controlled reactions at the interface. These results demonstrate that there is growing evidence for the critical role of excluded volume in interfacial regions in modifying the dimensionality of diffusive exploration.

2

(1)

To1

where is the relaxation time at very high frequency, A is a constant characterizing the strength of the dipolar couplings and the probability that the water proton is at the interface, τdiff is the correlation time for translational diffusion in the interface, τI is the lifetime for the interfacial coupling, and ω is the Larmor frequency.1 The solid line in Figure 1 is a fit to this equation, where the leading term is 1/To1 = 0.03 s−1; A is 1 × 107 s−2, τdiff is 71 ps, and τI is 6 μs. Although the relaxation derives from both the inside and outside of the vesicles, the water inside is trapped so that the correlations with the interfacial protons may be revisited until the escape event which finally defeats the correlation and creates the plateau at low field strength. We note that this “escape event” lifetime is not particularly well determined by these data and may be somewhat long for putative unilamellar vesicles. Furthermore, it is possible, or likely, that the plateau lifetime is influenced by the presence of a small population of multilamellar vesicles that are perhaps created by the sample impacts in the sample-shuttle-relaxation-dispersion instrument. Escape from the multilamellar spaces is expected to be slower than that from the interior of the vesicle. In either case, the slope of the high field portion of the dispersion provides a useful measurement of the correlation time for water diffusion in the interface. The translational correlation time is quite sensitive to the choice of the leading constant term, which depends on the residual proton concentration that derives from adventitious protons from the atmosphere. Our standard preparations

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AUTHOR INFORMATION

Corresponding Author

*Address: Chemistry Department, University of Virginia, P.O. Box 400319, Charlottesville, VA 22904-4319 USA. Phone: 434924-1494. E-mail: [email protected]. Fax: 434-924-3567. Notes

The authors declare no competing financial interest. 12477

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