Article pubs.acs.org/JPCB
Nanoscopic Dynamics of Phospholipid in Unilamellar Vesicles: Effect of Gel to Fluid Phase Transition V. K. Sharma,*,†,‡ E. Mamontov,§ D. B. Anunciado,† H. O’Neill,† and V. Urban† †
Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡ Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India § Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ABSTRACT: The dynamics of phospholipids in unilamellar vesicles (ULVs) is of interest in biology, medical, and food sciences, since these molecules are widely used as biocompatible agents and a mimic of cell membrane systems. We have investigated the nanoscopic dynamics of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) phospholipid in ULVs as a function of temperature using elastic and quasielastic neutron scattering (QENS). The dependence of the signal on the scattering momentum transfer, which is a critical advantage of neutron scattering techniques, allows the detailed analysis of the lipid motions that cannot be carried out by other means. In agreement with a differential scanning calorimetry measurement, a sharp rise in the elastic scattering intensity below ca. 296 K indicates a phase transition from the high-temperature fluid phase to the lowtemperature solid gel phase. The microscopic lipid dynamics exhibits qualitative differences between the solid gel phase (in a measurement at 280 K) and the fluid phase (in a measurement at a physiological temperature of 310 K). The analysis of the data demonstrates the presence of two types of distinct motions: the entire lipid molecule motion within a monolayer, also known as lateral diffusion, and the relatively faster internal motion of the DMPC molecule. The lateral diffusion of the entire lipid molecule is Fickian in character, whereas the internal lipid motions are of localized character, which is consistent with the structure of the vesicles. The lateral motion slows down by an order of magnitude in the solid gel phase, whereas for the internal motion not only the time scale but also the character of the motion changes upon the phase transition. In the solid gel phase, the lipids are more ordered and undergo uniaxial rotational motion. However, in the fluid phase, the hydrogen atoms of the lipid tails undergo confined translation diffusion rather than uniaxial rotational diffusion. The translational, but spatially localized, diffusion of the hydrogen atoms of the lipid tails is a manifestation of the flexibility of the chains acquired in the fluid phase. Because of this flexibility, both the local diffusivity and the confinement volume for the hydrogen atoms increase in the linear fashion from near the lipid’s polar headgroup to the end of its hydrophobic tail. Our results present a quantitative and detailed picture of the effect of the gel−fluid phase transition on the nanoscopic lipid dynamics in ULVs. The data analysis approach developed here has a potential for probing the dynamic response of lipids to the presence of additional cell membrane components.
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INTRODUCTION Lipid-based systems have been thoroughly studied in the past, as they are considered to be one of the four building blocks of life along with nucleic acids, proteins, and carbohydrates.1−3 Lipid molecules are amphiphilic in character, consisting of a hydrophilic headgroup and hydrophobic hydrocarbon tails. The amphiphilic nature of lipid molecules is what drives their selfassembly into different structures such as micelles, vesicles, bilayers, etc., in aqueous environments. A glycerophospholipid or phospholipid is composed of glycerol-based lipid, with two hydrocarbon chains, and a phosphate attached to the headgroup. Phospholipids prefer to form a bilayer structure when added in an aqueous solution. The phospholipid bilayer is the basic matrix that forms the biological membrane. The bilayer separates the interior of the cell from its surroundings, with the polar head groups in contact with the aqueous internal © 2015 American Chemical Society
and external environments of the cell and the lipid tails in the center of the bilayer forming its hydrophobic core. The macroscopic properties of such systems directly result from their behavior at the molecular structure level. These include the release rate of drug molecules from vesicles, enzymatic activity of the embedded proteins, and mechanical and permeability properties of the membrane. Therefore, it is of interest to pursue detailed insight into the dynamics on the molecular length scale in such systems, which is of importance for both basic scientific understanding and applications in the biological, pharmaceutical, and food industries. Singer and Nicolson4 have introduced the fluid mosaic model of lipid Received: January 8, 2015 Revised: March 3, 2015 Published: March 4, 2015 4460
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
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decades using the QENS technique.14−25 Pfeiffer et al.14 have carried out the first QENS measurements on a supported dipalmitoylphosphatidylcholine (DPPC) lipid bilayer and studied the local dynamics of lipid molecules to propose a description of lipid dynamics that included lateral motion, rotations, and librations. Tabony et al.15 have studied lateral motion of lipid molecules in phospholipid bilayers of DPPC to investigate the effect of temperature. It was broadly accepted that the dynamics of lipid molecules over the nearest neighbor distance could be described by a continuous diffusion process.14−16 However, in a recent paper by Busch et al.,17 a ballistic flow-like motion instead of traditionally quoted diffusive motion has been proposed to explain the overall long-range diffusion of phospholipid molecules in the membrane plane. It has been speculated that ballistic motion could represent a somewhat more efficient search strategy than continuous diffusion.17 Recently, it has been concluded by the Rheinstädter group21 that lateral motion of lipid molecules over the length scales exceeding the lipid’s diameter (∼2.37 Å) could be best described as a continuous diffusion, while the nature of the motion underwent a change on the length scale shorter than the nearest neighbor distance (2.4 Å).21 Thus, the scattering law describing the lateral motion becomes 4464
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
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the diffusion coefficient obtained in the solid gel phase (1.4 × 10−7 cm2/s). A QENS study carried out on hydrated powder of DMPC found that the lateral diffusion of DMPC molecules (5.2 × 10−7 cm2/s) was faster by a factor of 6 compared to the solid gel phase (0.86 × 10−7 cm2/s).39 We have compared our results with the reported diffusion coefficients for DMPC lipid molecules in different model membrane structures (such as supported, hydrated powder, multilamellar vesicles, etc.) and shown in Table 1. However, a direct comparison of the Table 1. Comparison of Lateral Diffusion Coefficients (Dlat) of DMPC Molecules in Various Models of Membrane as Obtained by the Microscopic QENS Technique at Different Temperatures phase solid gel (Lβ) fluid (Lα)
Figure 6. Typical S(Q, ω) for 5% (w/w) DMPV ULV in the fluid phase (310 K) fitted with the model scattering law given by eq 6.
T (K)
ΔE (μeV)
Dlat (×10−7 cm2/s)
5% (w/w) unilamellar vesicles, present study
280
3.4
0.7 ± 0.1
25% (w/w) hydrated powder, i.e., multi bilayer without support39 5% (w/w) unilamellar vesicles, present study supported single bilayer20 supported multi bilayers21 supported multi bilayers25 25% (w/w) hydrated powder, i.e., multi bilayer without support39 50% (w/w) hydrated powder, i.e., multi bilayer without support17
286
0.9
0.8
310
3.4
7.7 ± 0.3
303 310 303 308
3.4 8 20 0.9
6.0 6.4 12 5.2
303
4
4.4
313
60
18
model of membrane
diffusion coefficients is not straightforward, since the lipid dynamics depends on various factors such as hydration, temperature, and supported versus free-standing bilayers, and aqueous medium conditions. Moreover, the observed diffusion coefficient even for the same sample is known to depend on the spectrometer resolution, i.e., the microscopic observation time.17,46 It has been shown previously17 that, due to the main phase transition, the lateral motion of DMPC is not much affected on the 35 ps time scale, i.e., in a measurement on a QENS spectrometer with an energy resolution (ΔE) of 60 μeV. Conversely, with an increase in the observation time scale (i.e., better energy resolution), the diffusion coefficient in the same system decreases and tends toward the value obtained by macroscopic measurements.17,46 As the reported results are highly dependent on the time scale of observation, a careful interpretation is needed to explain the observed values of the diffusion coefficient. To highlight the effect of support on a substrate, we have compared the reported diffusion coefficient for DMPC lipid in a single bilayer of supported20 and nonsupported (e.g., in ULV) obtained with very similar observation times. Armstrong et al.20 have studied the dynamics of a supported single bilayer of DMPC in a fluid phase using the BASIS spectrometer with the same energy resolution as in the present work. The lateral diffusion coefficient for DMPC in the fluid phase in the supported single bilayer is 6 × 10−7 cm2/ s, which is slightly lower than the value obtained in this work (7.7 × 10−7 cm2/s). This may be due to the presence of a substrate, which could slightly restrict the diffusion in the supported bilayer. Moreover, Armstrong et al.20 have observed hopping diffusion of lipids through the nearest neighbor sites, whereas no signature of such a process has been observed in the present study. This may be due to a higher level of structural
Figure 7. Q-dependence of the HWHM, Γlat, corresponding to the lateral motion for DMPC lipid in ULV solid gel (280 K) and fluid (310 K) phase. The solid lines show the fits with Fick’s diffusion law.
280 K. It is found that the main phase transition is strongly correlated with the microscopic lateral motion of the lipid molecules. In the solid gel phase, the lipid molecules are more ordered and densely packed and therefore perform hindered lateral diffusion. It has been shown43 that due to the main phase transition the area per lipid molecule increases; i.e., the molecules become loosely packed and more disordered. These factors promote the movement of lipid molecules in the lateral direction. These observations are consistent with molecular dynamics (MD) simulations44 and FRAP results,45 which indicates that the mobility of phospholipid molecules is correlated with the area available per lipid molecule. These results are compared with earlier QENS observations on the hydrated lipid powders.15,39 The early QENS results on a hydrated powder of DPPC15 showed that the lateral diffusion coefficient of the DPPC molecules in the fluid phase was 12 × 10−7 cm2/s, which was nearly an order of magnitude faster than 4465
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The Journal of Physical Chemistry B order in the single supported bilayer that occurs as a result of substrate effects. The dynamics of DMPC in various model membrane systems had been studied using various macroscopic techniques, such as fluorescence spectroscopy, NMR, etc.2,7,12 An excellent comparison of the lateral diffusion coefficients for various membrane model systems as observed using different macroscopic techniques (such as FRAP, NMR, etc.) had been given in ref 7. FRAP measurements showed that the lateral motion in the solid gel phase is slower by nearly 3 orders of magnitude compared to that in the fluid phase.2,7 The reported lateral diffusion coefficient for DMPC in the fluid and solid gel phase was found to be ∼5 × 10−8 and ∼7 × 10−11 cm2/s, respectively. In contrast, our QENS results show that the lateral diffusion of DMPC in the fluid phase (7.7 × 10−7 cm2/s) is merely an order of magnitude faster compared to that in the solid gel phase (0.7 × 10−7 cm2/s). This disparity is due to the differences in the measurement of the diffusion mechanism at different length scales. As mentioned earlier, macroscopic techniques are sensitive to the diffusion mechanism on micrometer length scales (across hundreds of the lipid molecules), whereas microscopic techniques such as QENS are sensitive to the diffusion mechanism on a few nanometers length scale (close to a few nearest neighbors). It should be noted that the self -diffusion coefficient of whole vesicles will be much smaller than the diffusion coefficient for the lateral motion of the lipid molecules, and thus would not contribute to the observed data. The self-diffusion coefficient of a particle of radius R in a solution with a viscosity η at a temperature T can be estimated using the Stokes−Einstein relation, D = kBT/6πηR. For DMPC ULVs having a radius of 600 Å, the D of ∼0.17 × 10−7 cm2/s can be estimated using the viscosity of D2O at 280 K, ηD2O ∼1.98 cP.47 This value is lower, by a factor of 4, than the observed value for the diffusion coefficient of the lateral motion of the lipid molecules (0.7 × 10−7 cm2/s). Internal Motion. The internal motions of the lipid molecules are faster than the lateral motion. The width of the second Lorentzian in eq 6 is a sum of the widths of the lateral (Γlat) and internal motions (Γint). Since Γlat is already known, Γint is obtained by subtracting Γlat from the Γtot. The Qdependence of the HWHM (Γint) and EISF (A(Q)) provides an insight into the character of the internal motions. The variations of the extracted EISF and HWHM for the internal motions are shown in Figures 8 and 9, respectively. It is evident that the main phase transition also affects the internal motion of the lipid molecules. This is more obvious from the variation of Γint (Figure 9). In the solid gel phase, Γint is found to be almost constant with Q, which is a typical signature of a reorientation motion. Above the phase transition temperature, in the fluid phase, Γint increases with Q, having plateaus between a certain low Q value and zero. This is a signature of localized translational diffusion.26 Due to the complex structure of lipid molecules with a large number of hydrogen atoms, it is difficult to perform a quantitative analysis of the EISF and the HWHM. However, under some approximation, it is possible to perform an analysis of the EISF and HWHM by which one can get useful information along with some physical parameters. We have taken an assumption that the acyl chains mainly contribute to the internal motion of the lipid molecules. This assumption is based mainly on the following two facts: (i) the scattering signal of the acyl chain dominates (about 75% of the total
Figure 8. Variation of EISF for 5% (w/w) DMPC based ULV with Q in the solid gel (280 K) and fluid (310 K) phase. The solid lines show the EISF computed for uniaxial rotational and localized translational models as described in the text for the solid gel and fluid phase, respectively.
Figure 9. Variation of the HWHM of the Lorentzian representing the internal motion, Γint, with Q for the 5% (w/w) DMPC based ULV. The solid lines are the fits with uniaxial rotational and localized translational models for the solid gel (280 K) and fluid phase (310 K), respectively.
incoherent signal) and (ii) the head groups undergo fast (∼meV) and restricted localized motion,17 which will not contribute in the limited energy transfer window of the present measurements. Moreover, it has been shown24,37 that, in contrast to the acyl chains, the headgroup does not undergo a sharp melting transition, indicating that the main phase transition affects the acyl chain motions only. Therefore, it is of interest to investigate the nature of the acyl chain motions below and above the main phase transition temperature. In the solid gel phase, alkyl chains are predominantly in an all-trans conformation, and have a well-ordered arrangement with a dense packing, as shown in Figure 1. The least complex model for the alkyl chain motions compatible with the geometry of the DMPC molecule would be the reorientation of the alkyl chain about the main axis, which is known as uniaxial rotational diffusion. For a rigid molecule experiencing uniaxial rotational diffusion about the molecular axis, the hydrogens undergo rotation on a circle of a radius a.48 It is also conceivable that not all of the CH2 units in the acyl chains of the lipid molecules may contribute to the observable dynamics.14 Therefore, the generalized scattering law for the internal motion of the lipid molecules in the solid gel phase can be written as26,48,49 4466
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The Journal of Physical Chemistry B ⎡ Sint(Q , ω) = (1 − px )δ(ω) + px ⎢B0 (Qa)δ(ω) ⎢⎣ +
1 π
N−1
∑ Bn(Qa) n=1
⎤ ⎥ (1/τn)2 + ω 2 ⎥⎦
observed HWHM, Γint, quite well. At 280 K, the rotational diffusion coefficient of DMPC lipid molecules is found to be 14 ± 2 μeV. The rotational diffusion coefficient can be expressed in terms of jump rate probability (1/τ1), and using the energy− time conversion factor, E(μeV)·t(ns) = 0.658, τ1 is found to be (1.1 ± 0.1) × 10−10 s. As the temperature is increased, the lipid molecules undergo a solid gel to fluid phase transition at 296 K. This main phase transition introduces more gauche defects in the hydrocarbon chains, making the tails more mobile.22,43 As a result, various phenomena start taking place, including the reorientation of alkyl chains, large amplitude oscillations, enhancement of bending and stretching modes, etc. Due to the emergence of these various dynamic components, the hydrogen atoms of the CH2 unit start exhibiting the dynamics that can be described as spatially confined diffusion. In the first approximation, one may assume a spherical confinement volume shape. The scattering law for a process known as diffusion within a sphere has been obtained by Volino and Dianoux.50 The corresponding EISF is
1/τn
(7)
with Bn(Qa) =
1 N
N
⎛
∑ j0 ⎜⎝2Qa sin p=1
πp ⎞ ⎛ 2πnp ⎞ ⎟ cos⎜ ⎟ N⎠ ⎝ N ⎠
τn−1 = 2τ −1 sin 2(nπ /N )
(8) (9)
Here px is the fraction of hydrogen atoms that exhibit dynamics on the observation time scale, N is the number of sites equidistantly distributed on a circle of radius a, j0 is the spherical Bessel function of the zeroth order, and τ is the average time spent between the successive jumps. It has been demonstrated that, for Qa ≤ π, this scattering law describes the uniaxial rotational diffusion for N ≥ 6.49 The rotational diffusion constant, Dr, can then be presented as Dr =
⎛π⎞ 2 1 sin 2⎜ ⎟ = ⎝ ⎠ τ τ1 N
⎡ 3j (QR ) ⎤2 ⎥ EISF = A 00(Q ) = ⎢ 1 ⎣ QR ⎦
where R is the sphere radius and j1 is the first order spherical Bessel function. The flexibility of the long alkyl chain implies that the hydrogens along the chain move with different diffusivities while being confined in the spheres of different radii.16,17,24,28−30,51 One can consider various distributions for the radii and diffusivity, such as linear, Gaussian, log-normal, etc.17,24,25,29,51,52 Here we have adopted a linear distribution description, similar to the one employed to explain the dynamics of phospholipid molecules in a fluid phase.16,17,24 This model is appropriate, since it accounts for the fact that different hydrogen atoms along the DMPC chains undergo diffusive motions spanning significantly different volumes. As a result, the scattering law for alkyl chain motion can be written after modifying the Volino and Dianoux model50 as
(10)
and the model EISF can be written as B0 (Qa) =
1 N
N
⎛
∑ j0 ⎜⎝2Qa sin p=1
πp ⎞ ⎟ N⎠
(11)
We performed the summation for N = 12, a sufficiently large number (greater than 6), which was found adequate for adopting the uniaxial rotational diffusion model over the Q range of the current experiment. In view of a finite fraction of the immobile hydrogen atoms, the total elastic fraction becomes A(Q ) = px B0 (Qa) + (1 − px )
(13)
(12)
The parameters px and a are then obtained by the leastsquares fitting of the EISF with the model described by eqs 11 and 12. It is found that this model describes the observed EISF satisfactorily, as shown by the black solid line in Figure 8, and the values of px and a are obtained as 0. 58 and 1.78 Å, respectively. The a = 1.78 Å value is close to the average distance of the hydrogen atom from the molecular axis. The px = 0.58 value shows that 58% (on average) of the hydrogen atoms in a chain contributes to the dynamics measured at 280 K. Pfeiffer et al.14 have suggested a hindered uniaxial 3-fold rotation in the solid gel phase for a supported DPPC bilayer with a radius of gyration of 1.25 Å, which is smaller than the observed a = 1.78 Å. This difference might be attributed to either the longer tails in DPPC, associated with the higher rigidity, or the interactions with the substrate in the supported DPPC bilayer as opposed to the free-standing DMPC bilayer in our experiment. As expected for a localized reorientational motion, Γint is found to be independent of Q at 280 K (Figure 9). The value of the rotational diffusion constant Dr can be obtained by the least-squares fitting of the data assuming a uniaxial rotational diffusion model (eqs 7−10). The rotation radius a obtained from the EISF Q-dependence (Figure 8) is used as a fixed parameter in the fitting procedure. The solid black line at 280 K in Figure 9 shows that the uniaxial rotation model describes the
Sint(Q , ω) =
+
1 π
1 M
∑
M
⎡
i=1
⎢⎣
∑ ⎢A 00(QR i)δ(ω) (2l + 1)A nl(QR i)
{l , n} ≠ {0,0}
⎤ ⎥ [(xnl)2 Di /R i 2]2 + ω 2 ⎥⎦ (xnl)2 Di /R i 2
(14)
The first term here represents the elastic scattering, whereas the second term is the quasielastic component, composed of a series of Lorentzians. Aln(QRi) (n, l ≠ 0,0) and A00(QRi) are the quasielastic and elastic structure factors. For different n and l, Aln(QR) can be calculated using the values of xln listed in ref 50. Ri is the radius of the ith sphere, and can be expressed as Ri =
i−1 [R max − R min] + R min M−1
(15)
Di represents the diffusivity of hydrogens related to the ith site along the alkyl chain, and can be expressed as Di =
i−1 [Dmax − Dmin] + Dmin M−1
(16)
where M is the total number of CH2 units that are participating in the observed dynamics. For DMPC, we have taken M equal 4467
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
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Significant quasielastic broadening is observed for DMPC ULVs in both the solid gel and fluid phase. It is evident that there is a large increase in the QE broadening in the fluid phase of DMPC ULVs compared to that observed in the solid gel phase. Both the lateral and internal motions of lipid molecules contribute to the observed QENS data in both of the phases. It is found that the lateral motion in both of the phases is best described by a continuous diffusion model, and the diffusion coefficient obtained in the framework of this model is found to be larger in the fluid phase by an order of magnitude compared to that in the solid gel phase. This is in contrast with the macroscopic observation on ULVs, which indicates that the lateral diffusion coefficient in the solid gel phase is lower by at least 3 orders of magnitude compared to that in the fluid phase. This discrepancy is due to the observation on different time and length scales. Even for the same length scale, we have also pointed out that the effect of the phase transition on the lateral diffusion coefficient also depends on the observation time. A comparison of the lateral diffusion coefficient for DMPC molecules in various model membrane systems as observed by QENS indicates that the lateral diffusion in free-standing bilayers, such as in ULVs, is slightly faster than that in the supported bilayers. The phase transition affects not only the time scale but also the nature of the internal motion. In the solid gel phase, the observed data can be best described by uniaxial rotational motion about the molecular axis. On the other hand, in the fluid phase, acyl chains of lipid molecules undergo localized translational diffusion within the spheres of varying radius. The main goal of this work was to establish a framework for the data analysis of the lipid dynamics in both the solid gel and fluid phases. With this goal successfully achieved, the approach that we present here may be used in the future for the application of the same analysis to determine the dynamic response of lipids to the presence of additional cell membrane components.
to 14. Therefore, in the case when all of the CH2 units partake in the observable dynamics, the averaged EISF becomes A av (Q ) =
1 14
14
∑ A 00(QR i) = i=1
1 14
14
⎡ 3j (QR i) ⎤2 1 ⎥ ⎣ QR i ⎦
∑⎢ i=1
(17)
Within the framework of this model, the hydrogens associated with the CH2 unit closest to the lipid polar headgroup generate a sphere of the minimum radius Rmin and exhibit the smallest diffusion coefficient Dmin. As one moves progressively from the lipid polar headgroup toward the end of the hydrophobic alkyl chain, the diffusivity and the diffusion sphere radius increase. Finally, the hydrogens at the end of the hydrophobic tail (the CH3 unit) generate a sphere of the maximum radius Rmax and exhibit the largest diffusion coefficient Dmax. We have obtained the parameters Rmin and Rmax by the least-squares fit of the EISF at 310 K using eqs 15 and 17. The red solid line in Figure 8 (for 310 K) shows the so obtained fit. The values of Rmin and Rmax are found to be 0.04 and 5.15 Å, respectively. This suggests that the diffusion of hydrogen atoms in a DMPC lipid are confined to the spheres of radii between 0.04 and 5.15 Å. The unrealistically small value obtained for Rmin should be taken with reservation; it merely indicates negligible movement of the hydrogens in the first carbon position held by the headgroup. Similar models have been used to describe the dynamics of the lipid molecules in an unsupported multibilayer stack,17 and in an anhydrous phase.24 Busch et al.17 had observed two kinds of internal motions: slow segmental motion (few tens of μeV), which has been attributed mainly to the tail, and fast torsional motion (∼meV), which has been ascribed to the headgroup for DMPC molecules in 50% (w/w) hydrated multibilayer. Slow segmental motions are described with the similar model and in the fluid phase, and the Rmin and Rmax are obtained at 0.3 and 3.6 Å, respectively. The observed difference in the Rmax can be understood as an effect of the multibilayer, the difference in hydration, and the energy resolution of the spectrometer. Since there is no analytical expression for the HWHM of the QE component in the framework of the present model, one has to compute it numerically for given values of Rmin, Rmax, Dmin, and Dmax using eqs 14−16. The least-squares fitting method is employed to explain the observed quasielastic width corresponding to the internal motion with Dmin and Dmax as parameters, while the values of Rmin and Rmax are kept fixed as obtained from the fit of the EISF (Figure 8). The red solid line in Figure 9 (for 310 K) shows the so obtained fit. The values of Dmin and Dmax are found to be (0.3 ± 0.1) × 10−7 and (79 ± 7) × 10−7 cm2/s.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Phone: +1-865-243-1413. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Research conducted at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. The authors acknowledge the Center for Structural Molecular Biology supported by the Office of Biological and Environmental Research (ERKP291). This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy.
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CONCLUSIONS The dynamics of DMPC molecules in unilamellar vesicles, which is a mimic of a cell membrane, has been studied on a 400 ps observation time scale using elastic and high resolution quasielastic neutron scattering techniques in order to investigate the effect of the solid gel to fluid phase transition. Elastic intensity scans do not show any signature of a pretransition, i.e., solid gel to ripple phase transition (∼289 K), but they do show the main phase transition (solid gel to fluid phase) at 296 K. This indicates that on the 400 ps time scale there is no significant change in the dynamics due to the pretransition but there is a significant change associated with the main phase transition. The dynamical motions were observed in detail by quasielastic neutron scattering experiments in both solid gel (280 K) and fluid (310 K) phases.
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REFERENCES
(1) Campbell, A.; Reece, J. B. Biology, 8th ed.; Benjamin Cummings: San Francisco, CA, 2008. (2) Cevc, G., Ed. Phospholipids Handbook; Marcel Dekker: New York, 1993. (3) Fahy, E.; Subramaniam, S.; Brown, H. A.; Glass, C. K.; Merrill, A. H., Jr.; Murphy, R. C.; et al. A Comprehensive Classification System for Lipids. J. Lipid Res. 2005, 46, 839−862. (4) Singer, S. J.; Nicolson, G. L. The Fluid Mosaic Model of the Structure of Cell Membranes. Science 1972, 175 (4023), 720−731. (5) Grell, E. Membrane Spectroscopy; Springer Verlag: Berlin, 1981. 4468
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(27) Sharma, V. K.; Mitra, S.; Johnson, M.; Mukhopadhyay, R. Dynamics in Anionic Micelles: Effect of Phenyl Ring. J. Phys. Chem. B 2013, 117 (20), 6250−6255. (28) Sharma, V. K.; Mitra, S.; Garcia Sakai, V.; Hassan, P. A.; Peter Embs, J.; Mukhopadhyay, R. The Dynamical Landscape in CTAB Micelles. Soft Matter 2012, 8 (27), 7151−7160. (29) Sharma, V. K.; Mitra, S.; Garcia Sakai, V.; Mukhopadhyay, R. Dynamical Features in Cationic Micelles of Varied Chain Length. J. Phys. Chem. B 2012, 116 (30), 9007−9015. (30) Sharma, V. K.; Mitra, S.; Verma, G.; Hassan, P. A.; Garcia Sakai, V.; Mukhopadhyay, R. Internal Dynamics in SDS Micelles: Neutron Scattering Study. J. Phys. Chem. B 2010, 114 (51), 17049−17056. (31) Sharma, V. K.; Verma, G.; Gautam, S.; Hassan, P. A.; Mitra, S.; Mukhopadhyay, R. Monomer Dynamics in SDS Micellar Solution. Z. Phys. Chem. 2010, 224 (1−2), 253−261. (32) Vaz, W. L. C.; Almeida, P. F. Microscopic versus Macroscopic Diffusion in One-Component Fluid Phase Lipid Bilayer Membranes. Biophys. J. 1991, 60 (6), 1553−1554. (33) Rheinstadter, M. C.; Das, J.; Flenner, E. J.; Bruning, B.; Seydel, T.; Kosztin, I. Motional Coherence in Fluid Phospholipid Membranes. Phys. Rev. Lett. 2008, 101 (24), 248106−248106. (34) Falck, E.; Rog, T.; Karttunen, M.; Vattulainen, I. Lateral Diffusion in Lipid Membranes through Collective Flows. J. Am. Chem. Soc. 2008, 130 (1), 44−45. (35) Trapp, M.; Gutberlet, T.; Juranyi, F.; Unruh, T.; Deme, B.; Tehei, M.; Peters, J. Hydration Dependent Studies of Highly Aligned Multilayer Lipid Membranes by Neutron Scattering. J. Chem. Phys. 2010, 133 (16), 164505−164505. (36) Yi, Z.; Miao, Y.; Baudry, J.; Jain, N.; Smith, J. C. Derivation of Mean-Square Displacements for Protein Dynamics from Elastic Incoherent Neutron Scattering. J. Phys. Chem. B 2012, 116 (16), 5028−5036. (37) Rheinstädter, M. C.; Seydel, T.; Demmel, F.; Salditt, T. Molecular Motions in Lipid Bilayers Studied by the Neutron Backscattering Technique. Phys. Rev. E 2005, 71, 061908. (38) Trapp, M.; Marion, J.; Tehei, M.; Deme, B.; Gutberlet, T.; Peters, J. High Hydrostatic Pressure Effects Investigated by Neutron Scattering on Lipid Multilamellar Vesicles. Phys. Chem. Chem. Phys. 2013, 15 (48), 20951−20956. (39) Toppozini, L.; Armstrong, C. L.; Barrett, M. A.; Zheng, S.; Luo, L.; Nanda, H.; Sakai, V. G.; Rheinstadter, M. C. Partitioning of Ethanol into Lipid Membranes and Its Effect on Fluidity and Permeability as Seen by X-Ray and Neutron Scattering. Soft Matter 2012, 8 (47), 11839−11849. (40) Mamontov, E.; Herwig, K. W. A Time-of-Flight Backscattering Spectrometer at the Spallation Neutron Source, BASIS. Rev. Sci. Instrum. 2011, 82 (8), 085109. (41) Taylor, J.; Arnold, O.; Bilheaux, J.; Buts, A.; Campbell, S. Bull. Am. Phys. Soc. 2012, 57, W26.10. (42) Azuah, R. T.; Kneller, L. R.; Qiu, Y.; Tregenna-Piggott, P. L. W.; Brown, C. M.; Copley, J. R. D.; Dimeo, R. M. DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data. J. Res. Natl. Inst. Stand. Technol. 2009, 114, 341. (43) Nagle, J. F.; Tristram-Nagle, S. Structure of Lipid Bilayers. Biochim. Biophys. Acta, Rev. Biomembr. 2000, 1469 (3), 159−195. (44) Javanainen, M.; Monticelli, L.; Bernardino de la Serna, J.; Vattulainen, I. Free Volume Theory Applied to Lateral Diffusion in Langmuir Monolayers: Atomistic Simulations for a Protein-Free Model of Lung Surfactant. Langmuir 2010, 26 (19), 15436−15444. (45) Walder, R. B.; Honciuc, A.; Schwartz, D. K. Phospholipid Diffusion at the Oil-Water Interface. J. Phys. Chem. B 2010, 114 (35), 11484−11488. (46) Unruh, T.; Smuda, C.; Busch, S.; Neuhaus, J.; Petry, W. Diffusive Motions in Liquid Medium-Chain N-Alkanes as Seen by Quasielastic Time-of-Flight Neutron Spectroscopy. J. Chem. Phys. 2008, 129 (12), 121106−121106.
(6) Lipowsky, R.; Sackmann, E. Structure and Dynamics of Membranes. Handbook of Biological Physics; Elsevier, North Holland: Amsterdam, The Netherlands, 1995; Vol. 1. (7) Tocanne, J. F.; Dupou-Ciézanne, L.; Lopez, A. Lateral Diffusion of Lipids in Model and Natural Membranes. Prog. Lipid Res. 1994, 33, 203−237. (8) Perlo, J.; Meledandri, C. J.; Anoardo, E.; Brougham, D. F. Temperature and Size-Dependence of Membrane Molecular Dynamics in Unilamellar Vesicles by Fast Field-Cycling NMR Relaxometry. J. Phys. Chem. B 2011, 115 (13), 3444−3451. (9) Roberts, M. F.; Redfield, A. G.; Mohanty, U. Phospholipid Reorientation at the Lipid/Water Interface Measured by High Resolution 31P Field Cycling NMR Spectroscopy. Biophys. J. 2009, 97 (1), 132−141. (10) Pastor, R. W.; Venable, R. M.; Feller, S. E. Lipid Bilayers, NMR Relaxation, and Computer Simulations. Acc. Chem. Res. 2002, 35 (6), 438−446. (11) Kuo, A. L.; Wade, C. G. Lipid Lateral Diffusion by Pulsed Nuclear Magnetic Resonance. Biochemistry 1979, 18 (11), 2300−2308. (12) Macháň, R.; Hof, M. Lipid Diffusion in Planar Membranes Investigated by Fluorescence Correlation Spectroscopy. Biochim. Biophys. Acta 2010, 1798, 1377−1391. (13) Vaz, W. L. C.; Clegg, R. M.; Hallmann, D. Translational Diffusion of Lipids in Liquid Crystalline Phase Phosphatidylcholine Multibilayers: A Comparison of Experiment with Theory. Biochemistry 1985, 24, 781−786. (14) Pfeiffer, W.; Henkel, T.; Sackmann, E.; Knorr, W. Local Dynamics of Lipid Bilayers Studied by Incoherent Quasi-Elastic Neutron Scattering. Europhys. Lett. 1989, 8, 201−206. (15) Tabony, J.; Perly, B. Quasielastic Neutron Scattering Measurements of Fast Local Translational Diffusion of Lipid Molecules in Phospholipid Bilayers. Biochim. Biophys. Acta 1990, 1063, 67−72. (16) König, S.; Pfeiffer, W.; Bayerl, T.; Richter, D.; Sackmann, E. Molecular Dynamics of Lipid Bilayers Studied by Incoherent QuasiElastic Neutron Scattering. J. Phys. II 1992, 2, 1589−1615. (17) Busch, S.; Smuda, C.; Pardo, L. C.; Unruh, T. Molecular Mechanism of Long-Range Diffusion in Phospholipid Membranes Studied by Quasielastic Neutron Scattering. J. Am. Chem. Soc. 2010, 132 (10), 3232−3233. (18) Busch, S.; Unruh, T. The Slow Short-Time Motions of Phospholipid Molecules with a Focus on the Influence of Multiple Scattering and Fitting Artefacts. J. Phys.: Condens. Matter 2011, 23, 254205. (19) Busch, S.; Pardo, L. C.; Smuda, C.; Unruh, T. The Picosecond Dynamics of the Phospholipid Dimyristoylphosphatidylcholine in Mono- and Bilayers. Soft Matter 2012, 8 (13), 3576−3585. (20) Armstrong, C. L.; Kaye, M. D.; Zamponi, M.; Mamontov, E.; Tyagi, M.; Jenkins, T.; Rheinstadter, M. C. Diffusion in Single Supported Lipid Bilayers Studied by Quasi-Elastic Neutron Scattering. Soft Matter 2010, 6 (23), 5864−5867. (21) Armstrong, C. L.; Trapp, M.; Peters, J.; Seydel, T.; Rheinstädter, M. C. Short Range Ballistic Motion in Fluid Lipid Bilayers Studied by Quasi-Elastic Neutron Scattering. Soft Matter 2011, 7, 8358−8362. (22) Armstrong C. L. Diffusion and Domains: Membrane Structure and Dynamics Studied by Neutron Scattering. Doctoral Thesis, McMaster University, Canada, 2013. (23) Gerelli, Y.; Sakai, V. G.; Ollivier, J.; Deriu, A. Conformational and Segmental Dynamics in Lipid-Based Vesicles. Soft Matter 2011, 7 (8), 3929−3935. (24) Doxastakis, M.; Sakai, V. G.; Ohtake, S.; Maranas, J. K.; de Pablo, J. J. A Molecular View of Melting in Anhydrous Phospholipidic Membranes. Biophys. J. 2007, 92 (1), 147−161. (25) Wanderlingh, U.; D’Angelo, G.; Branca, C.; Nibali, V. C.; Trimarchi, A.; Rifici, S.; Finocchiaro, D.; Crupi, C.; Ollivier, J.; Middendorf, H. D. Multi-Component Modeling of Quasielastic Neutron Scattering from Phospholipid Membranes. J. Chem. Phys. 2014, 140 (17), 174901. (26) Bée, M. Quasielastic Neutron Scattering; Adam Hilger: Bristol, England, 1988. 4469
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
Article
The Journal of Physical Chemistry B (47) Hardy, R. C.; Cottington, R. L. Viscosity of Deuterium Oxide and Water From 5° to 125 °C. J. Res. Natl. Bur. Stand. 1949, 42, 573− 578. (48) Mitra, S.; Sharma, V. K.; Garcia Sakai, V.; Embs, J. P.; Mukhopadhyay, R. Molecular Mobility in Solid Sodium Dodecyl Sulfate. J. Phys. Chem. B 2011, 115 (32), 9732−9738. (49) Dianoux, A. J.; Volino, F.; Hervet, H. Incoherent Scattering Law for Neutron Quasi-Elastic Scattering in Liquid Crystals. Mol. Phys. 1975, 30 (4), 1181−1194. (50) Volino, F.; Dianoux, A. J. Neutron Incoherent Scattering Law for Diffusion in a Potential of Spherical Symmetry: General Formalism and Application to Diffusion Inside a Sphere. Mol. Phys. 1980, 41 (2), 271−279. (51) Carpentier, L.; Bée, M.; Giroud-Godquin, A. M.; Maldivi, P.; Marchon, J. C. Alkyl Chain Motions in Columnar Mesophases. Mol. Phys. 1989, 68 (6), 1367−1378. (52) Gibrat, G.; Assairi, F. L.; Blouquit, Y.; Craescu, C. T.; BellissentFunel, M. C. Biophysical Study of Thermal Denaturation of ApoCalmodulin: Dynamics of Native and Unfolded States. Biophys. J. 2008, 95 (11), 5247−5256.
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Nanoscopic Dynamics of Phospholipid in Unilamellar Vesicles: Effect of Gel to Fluid Phase Transition V. K. Sharma,*,†,‡ E. Mamontov,§ D. B. Anunciado,† H. O’Neill,† and V. Urban† †
Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡ Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India § Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ABSTRACT: The dynamics of phospholipids in unilamellar vesicles (ULVs) is of interest in biology, medical, and food sciences, since these molecules are widely used as biocompatible agents and a mimic of cell membrane systems. We have investigated the nanoscopic dynamics of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) phospholipid in ULVs as a function of temperature using elastic and quasielastic neutron scattering (QENS). The dependence of the signal on the scattering momentum transfer, which is a critical advantage of neutron scattering techniques, allows the detailed analysis of the lipid motions that cannot be carried out by other means. In agreement with a differential scanning calorimetry measurement, a sharp rise in the elastic scattering intensity below ca. 296 K indicates a phase transition from the high-temperature fluid phase to the lowtemperature solid gel phase. The microscopic lipid dynamics exhibits qualitative differences between the solid gel phase (in a measurement at 280 K) and the fluid phase (in a measurement at a physiological temperature of 310 K). The analysis of the data demonstrates the presence of two types of distinct motions: the entire lipid molecule motion within a monolayer, also known as lateral diffusion, and the relatively faster internal motion of the DMPC molecule. The lateral diffusion of the entire lipid molecule is Fickian in character, whereas the internal lipid motions are of localized character, which is consistent with the structure of the vesicles. The lateral motion slows down by an order of magnitude in the solid gel phase, whereas for the internal motion not only the time scale but also the character of the motion changes upon the phase transition. In the solid gel phase, the lipids are more ordered and undergo uniaxial rotational motion. However, in the fluid phase, the hydrogen atoms of the lipid tails undergo confined translation diffusion rather than uniaxial rotational diffusion. The translational, but spatially localized, diffusion of the hydrogen atoms of the lipid tails is a manifestation of the flexibility of the chains acquired in the fluid phase. Because of this flexibility, both the local diffusivity and the confinement volume for the hydrogen atoms increase in the linear fashion from near the lipid’s polar headgroup to the end of its hydrophobic tail. Our results present a quantitative and detailed picture of the effect of the gel−fluid phase transition on the nanoscopic lipid dynamics in ULVs. The data analysis approach developed here has a potential for probing the dynamic response of lipids to the presence of additional cell membrane components.
■
INTRODUCTION Lipid-based systems have been thoroughly studied in the past, as they are considered to be one of the four building blocks of life along with nucleic acids, proteins, and carbohydrates.1−3 Lipid molecules are amphiphilic in character, consisting of a hydrophilic headgroup and hydrophobic hydrocarbon tails. The amphiphilic nature of lipid molecules is what drives their selfassembly into different structures such as micelles, vesicles, bilayers, etc., in aqueous environments. A glycerophospholipid or phospholipid is composed of glycerol-based lipid, with two hydrocarbon chains, and a phosphate attached to the headgroup. Phospholipids prefer to form a bilayer structure when added in an aqueous solution. The phospholipid bilayer is the basic matrix that forms the biological membrane. The bilayer separates the interior of the cell from its surroundings, with the polar head groups in contact with the aqueous internal © 2015 American Chemical Society
and external environments of the cell and the lipid tails in the center of the bilayer forming its hydrophobic core. The macroscopic properties of such systems directly result from their behavior at the molecular structure level. These include the release rate of drug molecules from vesicles, enzymatic activity of the embedded proteins, and mechanical and permeability properties of the membrane. Therefore, it is of interest to pursue detailed insight into the dynamics on the molecular length scale in such systems, which is of importance for both basic scientific understanding and applications in the biological, pharmaceutical, and food industries. Singer and Nicolson4 have introduced the fluid mosaic model of lipid Received: January 8, 2015 Revised: March 3, 2015 Published: March 4, 2015 4460
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decades using the QENS technique.14−25 Pfeiffer et al.14 have carried out the first QENS measurements on a supported dipalmitoylphosphatidylcholine (DPPC) lipid bilayer and studied the local dynamics of lipid molecules to propose a description of lipid dynamics that included lateral motion, rotations, and librations. Tabony et al.15 have studied lateral motion of lipid molecules in phospholipid bilayers of DPPC to investigate the effect of temperature. It was broadly accepted that the dynamics of lipid molecules over the nearest neighbor distance could be described by a continuous diffusion process.14−16 However, in a recent paper by Busch et al.,17 a ballistic flow-like motion instead of traditionally quoted diffusive motion has been proposed to explain the overall long-range diffusion of phospholipid molecules in the membrane plane. It has been speculated that ballistic motion could represent a somewhat more efficient search strategy than continuous diffusion.17 Recently, it has been concluded by the Rheinstädter group21 that lateral motion of lipid molecules over the length scales exceeding the lipid’s diameter (∼2.37 Å) could be best described as a continuous diffusion, while the nature of the motion underwent a change on the length scale shorter than the nearest neighbor distance (2.4 Å).21 Thus, the scattering law describing the lateral motion becomes 4464
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the diffusion coefficient obtained in the solid gel phase (1.4 × 10−7 cm2/s). A QENS study carried out on hydrated powder of DMPC found that the lateral diffusion of DMPC molecules (5.2 × 10−7 cm2/s) was faster by a factor of 6 compared to the solid gel phase (0.86 × 10−7 cm2/s).39 We have compared our results with the reported diffusion coefficients for DMPC lipid molecules in different model membrane structures (such as supported, hydrated powder, multilamellar vesicles, etc.) and shown in Table 1. However, a direct comparison of the Table 1. Comparison of Lateral Diffusion Coefficients (Dlat) of DMPC Molecules in Various Models of Membrane as Obtained by the Microscopic QENS Technique at Different Temperatures phase solid gel (Lβ) fluid (Lα)
Figure 6. Typical S(Q, ω) for 5% (w/w) DMPV ULV in the fluid phase (310 K) fitted with the model scattering law given by eq 6.
T (K)
ΔE (μeV)
Dlat (×10−7 cm2/s)
5% (w/w) unilamellar vesicles, present study
280
3.4
0.7 ± 0.1
25% (w/w) hydrated powder, i.e., multi bilayer without support39 5% (w/w) unilamellar vesicles, present study supported single bilayer20 supported multi bilayers21 supported multi bilayers25 25% (w/w) hydrated powder, i.e., multi bilayer without support39 50% (w/w) hydrated powder, i.e., multi bilayer without support17
286
0.9
0.8
310
3.4
7.7 ± 0.3
303 310 303 308
3.4 8 20 0.9
6.0 6.4 12 5.2
303
4
4.4
313
60
18
model of membrane
diffusion coefficients is not straightforward, since the lipid dynamics depends on various factors such as hydration, temperature, and supported versus free-standing bilayers, and aqueous medium conditions. Moreover, the observed diffusion coefficient even for the same sample is known to depend on the spectrometer resolution, i.e., the microscopic observation time.17,46 It has been shown previously17 that, due to the main phase transition, the lateral motion of DMPC is not much affected on the 35 ps time scale, i.e., in a measurement on a QENS spectrometer with an energy resolution (ΔE) of 60 μeV. Conversely, with an increase in the observation time scale (i.e., better energy resolution), the diffusion coefficient in the same system decreases and tends toward the value obtained by macroscopic measurements.17,46 As the reported results are highly dependent on the time scale of observation, a careful interpretation is needed to explain the observed values of the diffusion coefficient. To highlight the effect of support on a substrate, we have compared the reported diffusion coefficient for DMPC lipid in a single bilayer of supported20 and nonsupported (e.g., in ULV) obtained with very similar observation times. Armstrong et al.20 have studied the dynamics of a supported single bilayer of DMPC in a fluid phase using the BASIS spectrometer with the same energy resolution as in the present work. The lateral diffusion coefficient for DMPC in the fluid phase in the supported single bilayer is 6 × 10−7 cm2/ s, which is slightly lower than the value obtained in this work (7.7 × 10−7 cm2/s). This may be due to the presence of a substrate, which could slightly restrict the diffusion in the supported bilayer. Moreover, Armstrong et al.20 have observed hopping diffusion of lipids through the nearest neighbor sites, whereas no signature of such a process has been observed in the present study. This may be due to a higher level of structural
Figure 7. Q-dependence of the HWHM, Γlat, corresponding to the lateral motion for DMPC lipid in ULV solid gel (280 K) and fluid (310 K) phase. The solid lines show the fits with Fick’s diffusion law.
280 K. It is found that the main phase transition is strongly correlated with the microscopic lateral motion of the lipid molecules. In the solid gel phase, the lipid molecules are more ordered and densely packed and therefore perform hindered lateral diffusion. It has been shown43 that due to the main phase transition the area per lipid molecule increases; i.e., the molecules become loosely packed and more disordered. These factors promote the movement of lipid molecules in the lateral direction. These observations are consistent with molecular dynamics (MD) simulations44 and FRAP results,45 which indicates that the mobility of phospholipid molecules is correlated with the area available per lipid molecule. These results are compared with earlier QENS observations on the hydrated lipid powders.15,39 The early QENS results on a hydrated powder of DPPC15 showed that the lateral diffusion coefficient of the DPPC molecules in the fluid phase was 12 × 10−7 cm2/s, which was nearly an order of magnitude faster than 4465
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The Journal of Physical Chemistry B order in the single supported bilayer that occurs as a result of substrate effects. The dynamics of DMPC in various model membrane systems had been studied using various macroscopic techniques, such as fluorescence spectroscopy, NMR, etc.2,7,12 An excellent comparison of the lateral diffusion coefficients for various membrane model systems as observed using different macroscopic techniques (such as FRAP, NMR, etc.) had been given in ref 7. FRAP measurements showed that the lateral motion in the solid gel phase is slower by nearly 3 orders of magnitude compared to that in the fluid phase.2,7 The reported lateral diffusion coefficient for DMPC in the fluid and solid gel phase was found to be ∼5 × 10−8 and ∼7 × 10−11 cm2/s, respectively. In contrast, our QENS results show that the lateral diffusion of DMPC in the fluid phase (7.7 × 10−7 cm2/s) is merely an order of magnitude faster compared to that in the solid gel phase (0.7 × 10−7 cm2/s). This disparity is due to the differences in the measurement of the diffusion mechanism at different length scales. As mentioned earlier, macroscopic techniques are sensitive to the diffusion mechanism on micrometer length scales (across hundreds of the lipid molecules), whereas microscopic techniques such as QENS are sensitive to the diffusion mechanism on a few nanometers length scale (close to a few nearest neighbors). It should be noted that the self -diffusion coefficient of whole vesicles will be much smaller than the diffusion coefficient for the lateral motion of the lipid molecules, and thus would not contribute to the observed data. The self-diffusion coefficient of a particle of radius R in a solution with a viscosity η at a temperature T can be estimated using the Stokes−Einstein relation, D = kBT/6πηR. For DMPC ULVs having a radius of 600 Å, the D of ∼0.17 × 10−7 cm2/s can be estimated using the viscosity of D2O at 280 K, ηD2O ∼1.98 cP.47 This value is lower, by a factor of 4, than the observed value for the diffusion coefficient of the lateral motion of the lipid molecules (0.7 × 10−7 cm2/s). Internal Motion. The internal motions of the lipid molecules are faster than the lateral motion. The width of the second Lorentzian in eq 6 is a sum of the widths of the lateral (Γlat) and internal motions (Γint). Since Γlat is already known, Γint is obtained by subtracting Γlat from the Γtot. The Qdependence of the HWHM (Γint) and EISF (A(Q)) provides an insight into the character of the internal motions. The variations of the extracted EISF and HWHM for the internal motions are shown in Figures 8 and 9, respectively. It is evident that the main phase transition also affects the internal motion of the lipid molecules. This is more obvious from the variation of Γint (Figure 9). In the solid gel phase, Γint is found to be almost constant with Q, which is a typical signature of a reorientation motion. Above the phase transition temperature, in the fluid phase, Γint increases with Q, having plateaus between a certain low Q value and zero. This is a signature of localized translational diffusion.26 Due to the complex structure of lipid molecules with a large number of hydrogen atoms, it is difficult to perform a quantitative analysis of the EISF and the HWHM. However, under some approximation, it is possible to perform an analysis of the EISF and HWHM by which one can get useful information along with some physical parameters. We have taken an assumption that the acyl chains mainly contribute to the internal motion of the lipid molecules. This assumption is based mainly on the following two facts: (i) the scattering signal of the acyl chain dominates (about 75% of the total
Figure 8. Variation of EISF for 5% (w/w) DMPC based ULV with Q in the solid gel (280 K) and fluid (310 K) phase. The solid lines show the EISF computed for uniaxial rotational and localized translational models as described in the text for the solid gel and fluid phase, respectively.
Figure 9. Variation of the HWHM of the Lorentzian representing the internal motion, Γint, with Q for the 5% (w/w) DMPC based ULV. The solid lines are the fits with uniaxial rotational and localized translational models for the solid gel (280 K) and fluid phase (310 K), respectively.
incoherent signal) and (ii) the head groups undergo fast (∼meV) and restricted localized motion,17 which will not contribute in the limited energy transfer window of the present measurements. Moreover, it has been shown24,37 that, in contrast to the acyl chains, the headgroup does not undergo a sharp melting transition, indicating that the main phase transition affects the acyl chain motions only. Therefore, it is of interest to investigate the nature of the acyl chain motions below and above the main phase transition temperature. In the solid gel phase, alkyl chains are predominantly in an all-trans conformation, and have a well-ordered arrangement with a dense packing, as shown in Figure 1. The least complex model for the alkyl chain motions compatible with the geometry of the DMPC molecule would be the reorientation of the alkyl chain about the main axis, which is known as uniaxial rotational diffusion. For a rigid molecule experiencing uniaxial rotational diffusion about the molecular axis, the hydrogens undergo rotation on a circle of a radius a.48 It is also conceivable that not all of the CH2 units in the acyl chains of the lipid molecules may contribute to the observable dynamics.14 Therefore, the generalized scattering law for the internal motion of the lipid molecules in the solid gel phase can be written as26,48,49 4466
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The Journal of Physical Chemistry B ⎡ Sint(Q , ω) = (1 − px )δ(ω) + px ⎢B0 (Qa)δ(ω) ⎢⎣ +
1 π
N−1
∑ Bn(Qa) n=1
⎤ ⎥ (1/τn)2 + ω 2 ⎥⎦
observed HWHM, Γint, quite well. At 280 K, the rotational diffusion coefficient of DMPC lipid molecules is found to be 14 ± 2 μeV. The rotational diffusion coefficient can be expressed in terms of jump rate probability (1/τ1), and using the energy− time conversion factor, E(μeV)·t(ns) = 0.658, τ1 is found to be (1.1 ± 0.1) × 10−10 s. As the temperature is increased, the lipid molecules undergo a solid gel to fluid phase transition at 296 K. This main phase transition introduces more gauche defects in the hydrocarbon chains, making the tails more mobile.22,43 As a result, various phenomena start taking place, including the reorientation of alkyl chains, large amplitude oscillations, enhancement of bending and stretching modes, etc. Due to the emergence of these various dynamic components, the hydrogen atoms of the CH2 unit start exhibiting the dynamics that can be described as spatially confined diffusion. In the first approximation, one may assume a spherical confinement volume shape. The scattering law for a process known as diffusion within a sphere has been obtained by Volino and Dianoux.50 The corresponding EISF is
1/τn
(7)
with Bn(Qa) =
1 N
N
⎛
∑ j0 ⎜⎝2Qa sin p=1
πp ⎞ ⎛ 2πnp ⎞ ⎟ cos⎜ ⎟ N⎠ ⎝ N ⎠
τn−1 = 2τ −1 sin 2(nπ /N )
(8) (9)
Here px is the fraction of hydrogen atoms that exhibit dynamics on the observation time scale, N is the number of sites equidistantly distributed on a circle of radius a, j0 is the spherical Bessel function of the zeroth order, and τ is the average time spent between the successive jumps. It has been demonstrated that, for Qa ≤ π, this scattering law describes the uniaxial rotational diffusion for N ≥ 6.49 The rotational diffusion constant, Dr, can then be presented as Dr =
⎛π⎞ 2 1 sin 2⎜ ⎟ = ⎝ ⎠ τ τ1 N
⎡ 3j (QR ) ⎤2 ⎥ EISF = A 00(Q ) = ⎢ 1 ⎣ QR ⎦
where R is the sphere radius and j1 is the first order spherical Bessel function. The flexibility of the long alkyl chain implies that the hydrogens along the chain move with different diffusivities while being confined in the spheres of different radii.16,17,24,28−30,51 One can consider various distributions for the radii and diffusivity, such as linear, Gaussian, log-normal, etc.17,24,25,29,51,52 Here we have adopted a linear distribution description, similar to the one employed to explain the dynamics of phospholipid molecules in a fluid phase.16,17,24 This model is appropriate, since it accounts for the fact that different hydrogen atoms along the DMPC chains undergo diffusive motions spanning significantly different volumes. As a result, the scattering law for alkyl chain motion can be written after modifying the Volino and Dianoux model50 as
(10)
and the model EISF can be written as B0 (Qa) =
1 N
N
⎛
∑ j0 ⎜⎝2Qa sin p=1
πp ⎞ ⎟ N⎠
(11)
We performed the summation for N = 12, a sufficiently large number (greater than 6), which was found adequate for adopting the uniaxial rotational diffusion model over the Q range of the current experiment. In view of a finite fraction of the immobile hydrogen atoms, the total elastic fraction becomes A(Q ) = px B0 (Qa) + (1 − px )
(13)
(12)
The parameters px and a are then obtained by the leastsquares fitting of the EISF with the model described by eqs 11 and 12. It is found that this model describes the observed EISF satisfactorily, as shown by the black solid line in Figure 8, and the values of px and a are obtained as 0. 58 and 1.78 Å, respectively. The a = 1.78 Å value is close to the average distance of the hydrogen atom from the molecular axis. The px = 0.58 value shows that 58% (on average) of the hydrogen atoms in a chain contributes to the dynamics measured at 280 K. Pfeiffer et al.14 have suggested a hindered uniaxial 3-fold rotation in the solid gel phase for a supported DPPC bilayer with a radius of gyration of 1.25 Å, which is smaller than the observed a = 1.78 Å. This difference might be attributed to either the longer tails in DPPC, associated with the higher rigidity, or the interactions with the substrate in the supported DPPC bilayer as opposed to the free-standing DMPC bilayer in our experiment. As expected for a localized reorientational motion, Γint is found to be independent of Q at 280 K (Figure 9). The value of the rotational diffusion constant Dr can be obtained by the least-squares fitting of the data assuming a uniaxial rotational diffusion model (eqs 7−10). The rotation radius a obtained from the EISF Q-dependence (Figure 8) is used as a fixed parameter in the fitting procedure. The solid black line at 280 K in Figure 9 shows that the uniaxial rotation model describes the
Sint(Q , ω) =
+
1 π
1 M
∑
M
⎡
i=1
⎢⎣
∑ ⎢A 00(QR i)δ(ω) (2l + 1)A nl(QR i)
{l , n} ≠ {0,0}
⎤ ⎥ [(xnl)2 Di /R i 2]2 + ω 2 ⎥⎦ (xnl)2 Di /R i 2
(14)
The first term here represents the elastic scattering, whereas the second term is the quasielastic component, composed of a series of Lorentzians. Aln(QRi) (n, l ≠ 0,0) and A00(QRi) are the quasielastic and elastic structure factors. For different n and l, Aln(QR) can be calculated using the values of xln listed in ref 50. Ri is the radius of the ith sphere, and can be expressed as Ri =
i−1 [R max − R min] + R min M−1
(15)
Di represents the diffusivity of hydrogens related to the ith site along the alkyl chain, and can be expressed as Di =
i−1 [Dmax − Dmin] + Dmin M−1
(16)
where M is the total number of CH2 units that are participating in the observed dynamics. For DMPC, we have taken M equal 4467
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
Article
The Journal of Physical Chemistry B
Significant quasielastic broadening is observed for DMPC ULVs in both the solid gel and fluid phase. It is evident that there is a large increase in the QE broadening in the fluid phase of DMPC ULVs compared to that observed in the solid gel phase. Both the lateral and internal motions of lipid molecules contribute to the observed QENS data in both of the phases. It is found that the lateral motion in both of the phases is best described by a continuous diffusion model, and the diffusion coefficient obtained in the framework of this model is found to be larger in the fluid phase by an order of magnitude compared to that in the solid gel phase. This is in contrast with the macroscopic observation on ULVs, which indicates that the lateral diffusion coefficient in the solid gel phase is lower by at least 3 orders of magnitude compared to that in the fluid phase. This discrepancy is due to the observation on different time and length scales. Even for the same length scale, we have also pointed out that the effect of the phase transition on the lateral diffusion coefficient also depends on the observation time. A comparison of the lateral diffusion coefficient for DMPC molecules in various model membrane systems as observed by QENS indicates that the lateral diffusion in free-standing bilayers, such as in ULVs, is slightly faster than that in the supported bilayers. The phase transition affects not only the time scale but also the nature of the internal motion. In the solid gel phase, the observed data can be best described by uniaxial rotational motion about the molecular axis. On the other hand, in the fluid phase, acyl chains of lipid molecules undergo localized translational diffusion within the spheres of varying radius. The main goal of this work was to establish a framework for the data analysis of the lipid dynamics in both the solid gel and fluid phases. With this goal successfully achieved, the approach that we present here may be used in the future for the application of the same analysis to determine the dynamic response of lipids to the presence of additional cell membrane components.
to 14. Therefore, in the case when all of the CH2 units partake in the observable dynamics, the averaged EISF becomes A av (Q ) =
1 14
14
∑ A 00(QR i) = i=1
1 14
14
⎡ 3j (QR i) ⎤2 1 ⎥ ⎣ QR i ⎦
∑⎢ i=1
(17)
Within the framework of this model, the hydrogens associated with the CH2 unit closest to the lipid polar headgroup generate a sphere of the minimum radius Rmin and exhibit the smallest diffusion coefficient Dmin. As one moves progressively from the lipid polar headgroup toward the end of the hydrophobic alkyl chain, the diffusivity and the diffusion sphere radius increase. Finally, the hydrogens at the end of the hydrophobic tail (the CH3 unit) generate a sphere of the maximum radius Rmax and exhibit the largest diffusion coefficient Dmax. We have obtained the parameters Rmin and Rmax by the least-squares fit of the EISF at 310 K using eqs 15 and 17. The red solid line in Figure 8 (for 310 K) shows the so obtained fit. The values of Rmin and Rmax are found to be 0.04 and 5.15 Å, respectively. This suggests that the diffusion of hydrogen atoms in a DMPC lipid are confined to the spheres of radii between 0.04 and 5.15 Å. The unrealistically small value obtained for Rmin should be taken with reservation; it merely indicates negligible movement of the hydrogens in the first carbon position held by the headgroup. Similar models have been used to describe the dynamics of the lipid molecules in an unsupported multibilayer stack,17 and in an anhydrous phase.24 Busch et al.17 had observed two kinds of internal motions: slow segmental motion (few tens of μeV), which has been attributed mainly to the tail, and fast torsional motion (∼meV), which has been ascribed to the headgroup for DMPC molecules in 50% (w/w) hydrated multibilayer. Slow segmental motions are described with the similar model and in the fluid phase, and the Rmin and Rmax are obtained at 0.3 and 3.6 Å, respectively. The observed difference in the Rmax can be understood as an effect of the multibilayer, the difference in hydration, and the energy resolution of the spectrometer. Since there is no analytical expression for the HWHM of the QE component in the framework of the present model, one has to compute it numerically for given values of Rmin, Rmax, Dmin, and Dmax using eqs 14−16. The least-squares fitting method is employed to explain the observed quasielastic width corresponding to the internal motion with Dmin and Dmax as parameters, while the values of Rmin and Rmax are kept fixed as obtained from the fit of the EISF (Figure 8). The red solid line in Figure 9 (for 310 K) shows the so obtained fit. The values of Dmin and Dmax are found to be (0.3 ± 0.1) × 10−7 and (79 ± 7) × 10−7 cm2/s.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Phone: +1-865-243-1413. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS Research conducted at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. The authors acknowledge the Center for Structural Molecular Biology supported by the Office of Biological and Environmental Research (ERKP291). This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy.
■
CONCLUSIONS The dynamics of DMPC molecules in unilamellar vesicles, which is a mimic of a cell membrane, has been studied on a 400 ps observation time scale using elastic and high resolution quasielastic neutron scattering techniques in order to investigate the effect of the solid gel to fluid phase transition. Elastic intensity scans do not show any signature of a pretransition, i.e., solid gel to ripple phase transition (∼289 K), but they do show the main phase transition (solid gel to fluid phase) at 296 K. This indicates that on the 400 ps time scale there is no significant change in the dynamics due to the pretransition but there is a significant change associated with the main phase transition. The dynamical motions were observed in detail by quasielastic neutron scattering experiments in both solid gel (280 K) and fluid (310 K) phases.
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REFERENCES
(1) Campbell, A.; Reece, J. B. Biology, 8th ed.; Benjamin Cummings: San Francisco, CA, 2008. (2) Cevc, G., Ed. Phospholipids Handbook; Marcel Dekker: New York, 1993. (3) Fahy, E.; Subramaniam, S.; Brown, H. A.; Glass, C. K.; Merrill, A. H., Jr.; Murphy, R. C.; et al. A Comprehensive Classification System for Lipids. J. Lipid Res. 2005, 46, 839−862. (4) Singer, S. J.; Nicolson, G. L. The Fluid Mosaic Model of the Structure of Cell Membranes. Science 1972, 175 (4023), 720−731. (5) Grell, E. Membrane Spectroscopy; Springer Verlag: Berlin, 1981. 4468
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
Article
The Journal of Physical Chemistry B
(27) Sharma, V. K.; Mitra, S.; Johnson, M.; Mukhopadhyay, R. Dynamics in Anionic Micelles: Effect of Phenyl Ring. J. Phys. Chem. B 2013, 117 (20), 6250−6255. (28) Sharma, V. K.; Mitra, S.; Garcia Sakai, V.; Hassan, P. A.; Peter Embs, J.; Mukhopadhyay, R. The Dynamical Landscape in CTAB Micelles. Soft Matter 2012, 8 (27), 7151−7160. (29) Sharma, V. K.; Mitra, S.; Garcia Sakai, V.; Mukhopadhyay, R. Dynamical Features in Cationic Micelles of Varied Chain Length. J. Phys. Chem. B 2012, 116 (30), 9007−9015. (30) Sharma, V. K.; Mitra, S.; Verma, G.; Hassan, P. A.; Garcia Sakai, V.; Mukhopadhyay, R. Internal Dynamics in SDS Micelles: Neutron Scattering Study. J. Phys. Chem. B 2010, 114 (51), 17049−17056. (31) Sharma, V. K.; Verma, G.; Gautam, S.; Hassan, P. A.; Mitra, S.; Mukhopadhyay, R. Monomer Dynamics in SDS Micellar Solution. Z. Phys. Chem. 2010, 224 (1−2), 253−261. (32) Vaz, W. L. C.; Almeida, P. F. Microscopic versus Macroscopic Diffusion in One-Component Fluid Phase Lipid Bilayer Membranes. Biophys. J. 1991, 60 (6), 1553−1554. (33) Rheinstadter, M. C.; Das, J.; Flenner, E. J.; Bruning, B.; Seydel, T.; Kosztin, I. Motional Coherence in Fluid Phospholipid Membranes. Phys. Rev. Lett. 2008, 101 (24), 248106−248106. (34) Falck, E.; Rog, T.; Karttunen, M.; Vattulainen, I. Lateral Diffusion in Lipid Membranes through Collective Flows. J. Am. Chem. Soc. 2008, 130 (1), 44−45. (35) Trapp, M.; Gutberlet, T.; Juranyi, F.; Unruh, T.; Deme, B.; Tehei, M.; Peters, J. Hydration Dependent Studies of Highly Aligned Multilayer Lipid Membranes by Neutron Scattering. J. Chem. Phys. 2010, 133 (16), 164505−164505. (36) Yi, Z.; Miao, Y.; Baudry, J.; Jain, N.; Smith, J. C. Derivation of Mean-Square Displacements for Protein Dynamics from Elastic Incoherent Neutron Scattering. J. Phys. Chem. B 2012, 116 (16), 5028−5036. (37) Rheinstädter, M. C.; Seydel, T.; Demmel, F.; Salditt, T. Molecular Motions in Lipid Bilayers Studied by the Neutron Backscattering Technique. Phys. Rev. E 2005, 71, 061908. (38) Trapp, M.; Marion, J.; Tehei, M.; Deme, B.; Gutberlet, T.; Peters, J. High Hydrostatic Pressure Effects Investigated by Neutron Scattering on Lipid Multilamellar Vesicles. Phys. Chem. Chem. Phys. 2013, 15 (48), 20951−20956. (39) Toppozini, L.; Armstrong, C. L.; Barrett, M. A.; Zheng, S.; Luo, L.; Nanda, H.; Sakai, V. G.; Rheinstadter, M. C. Partitioning of Ethanol into Lipid Membranes and Its Effect on Fluidity and Permeability as Seen by X-Ray and Neutron Scattering. Soft Matter 2012, 8 (47), 11839−11849. (40) Mamontov, E.; Herwig, K. W. A Time-of-Flight Backscattering Spectrometer at the Spallation Neutron Source, BASIS. Rev. Sci. Instrum. 2011, 82 (8), 085109. (41) Taylor, J.; Arnold, O.; Bilheaux, J.; Buts, A.; Campbell, S. Bull. Am. Phys. Soc. 2012, 57, W26.10. (42) Azuah, R. T.; Kneller, L. R.; Qiu, Y.; Tregenna-Piggott, P. L. W.; Brown, C. M.; Copley, J. R. D.; Dimeo, R. M. DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data. J. Res. Natl. Inst. Stand. Technol. 2009, 114, 341. (43) Nagle, J. F.; Tristram-Nagle, S. Structure of Lipid Bilayers. Biochim. Biophys. Acta, Rev. Biomembr. 2000, 1469 (3), 159−195. (44) Javanainen, M.; Monticelli, L.; Bernardino de la Serna, J.; Vattulainen, I. Free Volume Theory Applied to Lateral Diffusion in Langmuir Monolayers: Atomistic Simulations for a Protein-Free Model of Lung Surfactant. Langmuir 2010, 26 (19), 15436−15444. (45) Walder, R. B.; Honciuc, A.; Schwartz, D. K. Phospholipid Diffusion at the Oil-Water Interface. J. Phys. Chem. B 2010, 114 (35), 11484−11488. (46) Unruh, T.; Smuda, C.; Busch, S.; Neuhaus, J.; Petry, W. Diffusive Motions in Liquid Medium-Chain N-Alkanes as Seen by Quasielastic Time-of-Flight Neutron Spectroscopy. J. Chem. Phys. 2008, 129 (12), 121106−121106.
(6) Lipowsky, R.; Sackmann, E. Structure and Dynamics of Membranes. Handbook of Biological Physics; Elsevier, North Holland: Amsterdam, The Netherlands, 1995; Vol. 1. (7) Tocanne, J. F.; Dupou-Ciézanne, L.; Lopez, A. Lateral Diffusion of Lipids in Model and Natural Membranes. Prog. Lipid Res. 1994, 33, 203−237. (8) Perlo, J.; Meledandri, C. J.; Anoardo, E.; Brougham, D. F. Temperature and Size-Dependence of Membrane Molecular Dynamics in Unilamellar Vesicles by Fast Field-Cycling NMR Relaxometry. J. Phys. Chem. B 2011, 115 (13), 3444−3451. (9) Roberts, M. F.; Redfield, A. G.; Mohanty, U. Phospholipid Reorientation at the Lipid/Water Interface Measured by High Resolution 31P Field Cycling NMR Spectroscopy. Biophys. J. 2009, 97 (1), 132−141. (10) Pastor, R. W.; Venable, R. M.; Feller, S. E. Lipid Bilayers, NMR Relaxation, and Computer Simulations. Acc. Chem. Res. 2002, 35 (6), 438−446. (11) Kuo, A. L.; Wade, C. G. Lipid Lateral Diffusion by Pulsed Nuclear Magnetic Resonance. Biochemistry 1979, 18 (11), 2300−2308. (12) Macháň, R.; Hof, M. Lipid Diffusion in Planar Membranes Investigated by Fluorescence Correlation Spectroscopy. Biochim. Biophys. Acta 2010, 1798, 1377−1391. (13) Vaz, W. L. C.; Clegg, R. M.; Hallmann, D. Translational Diffusion of Lipids in Liquid Crystalline Phase Phosphatidylcholine Multibilayers: A Comparison of Experiment with Theory. Biochemistry 1985, 24, 781−786. (14) Pfeiffer, W.; Henkel, T.; Sackmann, E.; Knorr, W. Local Dynamics of Lipid Bilayers Studied by Incoherent Quasi-Elastic Neutron Scattering. Europhys. Lett. 1989, 8, 201−206. (15) Tabony, J.; Perly, B. Quasielastic Neutron Scattering Measurements of Fast Local Translational Diffusion of Lipid Molecules in Phospholipid Bilayers. Biochim. Biophys. Acta 1990, 1063, 67−72. (16) König, S.; Pfeiffer, W.; Bayerl, T.; Richter, D.; Sackmann, E. Molecular Dynamics of Lipid Bilayers Studied by Incoherent QuasiElastic Neutron Scattering. J. Phys. II 1992, 2, 1589−1615. (17) Busch, S.; Smuda, C.; Pardo, L. C.; Unruh, T. Molecular Mechanism of Long-Range Diffusion in Phospholipid Membranes Studied by Quasielastic Neutron Scattering. J. Am. Chem. Soc. 2010, 132 (10), 3232−3233. (18) Busch, S.; Unruh, T. The Slow Short-Time Motions of Phospholipid Molecules with a Focus on the Influence of Multiple Scattering and Fitting Artefacts. J. Phys.: Condens. Matter 2011, 23, 254205. (19) Busch, S.; Pardo, L. C.; Smuda, C.; Unruh, T. The Picosecond Dynamics of the Phospholipid Dimyristoylphosphatidylcholine in Mono- and Bilayers. Soft Matter 2012, 8 (13), 3576−3585. (20) Armstrong, C. L.; Kaye, M. D.; Zamponi, M.; Mamontov, E.; Tyagi, M.; Jenkins, T.; Rheinstadter, M. C. Diffusion in Single Supported Lipid Bilayers Studied by Quasi-Elastic Neutron Scattering. Soft Matter 2010, 6 (23), 5864−5867. (21) Armstrong, C. L.; Trapp, M.; Peters, J.; Seydel, T.; Rheinstädter, M. C. Short Range Ballistic Motion in Fluid Lipid Bilayers Studied by Quasi-Elastic Neutron Scattering. Soft Matter 2011, 7, 8358−8362. (22) Armstrong C. L. Diffusion and Domains: Membrane Structure and Dynamics Studied by Neutron Scattering. Doctoral Thesis, McMaster University, Canada, 2013. (23) Gerelli, Y.; Sakai, V. G.; Ollivier, J.; Deriu, A. Conformational and Segmental Dynamics in Lipid-Based Vesicles. Soft Matter 2011, 7 (8), 3929−3935. (24) Doxastakis, M.; Sakai, V. G.; Ohtake, S.; Maranas, J. K.; de Pablo, J. J. A Molecular View of Melting in Anhydrous Phospholipidic Membranes. Biophys. J. 2007, 92 (1), 147−161. (25) Wanderlingh, U.; D’Angelo, G.; Branca, C.; Nibali, V. C.; Trimarchi, A.; Rifici, S.; Finocchiaro, D.; Crupi, C.; Ollivier, J.; Middendorf, H. D. Multi-Component Modeling of Quasielastic Neutron Scattering from Phospholipid Membranes. J. Chem. Phys. 2014, 140 (17), 174901. (26) Bée, M. Quasielastic Neutron Scattering; Adam Hilger: Bristol, England, 1988. 4469
DOI: 10.1021/acs.jpcb.5b00220 J. Phys. Chem. B 2015, 119, 4460−4470
Article
The Journal of Physical Chemistry B (47) Hardy, R. C.; Cottington, R. L. Viscosity of Deuterium Oxide and Water From 5° to 125 °C. J. Res. Natl. Bur. Stand. 1949, 42, 573− 578. (48) Mitra, S.; Sharma, V. K.; Garcia Sakai, V.; Embs, J. P.; Mukhopadhyay, R. Molecular Mobility in Solid Sodium Dodecyl Sulfate. J. Phys. Chem. B 2011, 115 (32), 9732−9738. (49) Dianoux, A. J.; Volino, F.; Hervet, H. Incoherent Scattering Law for Neutron Quasi-Elastic Scattering in Liquid Crystals. Mol. Phys. 1975, 30 (4), 1181−1194. (50) Volino, F.; Dianoux, A. J. Neutron Incoherent Scattering Law for Diffusion in a Potential of Spherical Symmetry: General Formalism and Application to Diffusion Inside a Sphere. Mol. Phys. 1980, 41 (2), 271−279. (51) Carpentier, L.; Bée, M.; Giroud-Godquin, A. M.; Maldivi, P.; Marchon, J. C. Alkyl Chain Motions in Columnar Mesophases. Mol. Phys. 1989, 68 (6), 1367−1378. (52) Gibrat, G.; Assairi, F. L.; Blouquit, Y.; Craescu, C. T.; BellissentFunel, M. C. Biophysical Study of Thermal Denaturation of ApoCalmodulin: Dynamics of Native and Unfolded States. Biophys. J. 2008, 95 (11), 5247−5256.
4470
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