Temperature and Hydration Dependence of Low-Frequency Spectra

Article pubs.acs.org/JPCB

Temperature and Hydration Dependence of Low-Frequency Spectra of Lipid Bilayers Studied by Terahertz Time-Domain Spectroscopy Naoki Yamamoto,† Tomoyo Andachi,‡ Atsuo Tamura,‡ and Keisuke Tominaga*,†,‡ †

Molecular Photoscience Research Center and ‡Graduate School of Science, Kobe University, Rokkodai-cho 1-1, Nada, Kobe 657-8501, Japan ABSTRACT: We have studied temperature and hydration dependent lowfrequency spectra of lipid bilayers of 1,2-dimyristoyl-sn-glycero-3-phosphoryl-3′rac-glycerol (DMPG) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) by terahertz time-domain spectroscopy (THz-TDS). We measured X-ray diffraction patterns and mid-infrared spectra of these lipid bilayers and found that the lipid bilayers have two different types of phases, i.e., the gel phase and the crystalline phase, depending on the preparation methods of the samples. In both phases, a few distinct bands were observed in the THz region. For DMPG, the peak wavenumbers of the absorption bands did not change upon hydration, while the bandwidth in the crystalline phase was smaller than that in the gel phase. We performed spectral analyses for the complex dielectric spectra for DMPG and DMPC with a model function, mainly to determine the peak wavenumbers of the absorption bands. In contrast to the case of the DMPG bilayers, the peak wavenumber of the absorption band of the DMPC bilayer shifts upon hydration. In the hydrated DMPC bilayer, it was suggested fast reorienting water molecules exist with a relaxation time of sub-picoseconds. It is suggested that the THz absorption patterns reflect the lipid packing pattern in the bilayers. The temperature dependence of the absorption band was analyzed by an empirical equation, and the anharmonicity of the vibrational potential of the low-frequency mode was quantitatively evaluated.

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molecules.17 Choi et al. monitored a phase transition of a lipid bilayer by THz time-domain spectroscopy (TDS) and found that the dynamics of hydrating water were correlated with the transition.18 Hishida and Tanaka estimated the number of hydrating water molecules and suggested that the hydration effect reaches 4−5 water layers on the bilayer surface.19 Recently, we performed THz-TDS on a lipid bilayer composed of a zwitter ionic phospholipid, 1,2-dimyristoyl-sn-glycero-3phosphocholine (DMPC, Figure 1A) with changing temperature and hydration level. We observed several absorption bands in the THz frequency region, and the peak wavenumbers of the bands change upon hydration.20 The result suggests that THz spectroscopy can be used as a tool to obtain structural and dynamical information on lipid bilayers. In this paper, we study the temperature and hydration dependence of the THz spectra of the lipid bilayer of 1,2dimyristoyl-sn-glycero-3-phosphoryl-3′-rac-glycerol (DMPG) sodium salt (Figure 1B). This lipid has the same saturated hydrocarbon structures as DMPC (Figure 1A), while their hydrophilic head parts have different chemical groups. Because of these structural differences, it is expected that the THz spectra of DMPG show different characteristics from those of DMPC. Furthermore, we can prepare both the crystalline phase

INTRODUCTION Lipid bilayer is a main constituent of the cell wall of living systems to maintain the structure of the cell. In addition to this, it plays an important role in performing function to keep life activity such as ion and molecule transportation. Thus, it is essential to understand its structural and dynamical properties relating to the functions. The lipid bilayer is surrounded by water in the cell, and the structural and dynamical properties are influenced by the interaction with hydrating water molecules. Previously, spectroscopic studies were performed on lipid bilayers by X-ray scattering,1 dielectric spectroscopy,2−5 EPR,6 Raman scattering,7,8 ultrafast infrared pump−probe spectroscopy,9 neutron scattering,10,11 NMR,12−14 and molecular dynamics simulation.15 In these studies, special attention has been made to investigate the effects of water on the properties of lipid bilayers. These two decades have witnessed substantial progress in spectroscopic studies in the terahertz (THz) frequency region, which has been enabled by technical advances in generating and detecting pulsed radiation in the THz region.16 Since THz spectroscopy monitors dynamics in the sub-picosecond to picosecond region, this technique is expected to be a powerful tool to investigate the low-frequency vibrational modes and dielectric relaxation of bilayer and hydrating water. Previously, the low-frequency response of lipid bilayers and the hydrating water has been studied by THz spectroscopy. For example, Tielrooij et al. suggested dielectric relaxation modes of hydrating water in the THz region can be categorized into bulk-like water, irrotational water, and fast reorienting water © XXXX American Chemical Society

Special Issue: Branka M. Ladanyi Festschrift Received: October 2, 2014 Revised: December 4, 2014

A

dx.doi.org/10.1021/jp5099766 | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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crystalline phase. The gel-phase sample was prepared by the following procedure:21 in brief, the DMPG powder was dissolved in a mixture of chloroform:methanol = 2:1 (v/v), and then, the solvent was mildly evaporated with flowing dried nitrogen gas. To completely remove the solvent, the sample was left in a vacuum overnight. As a result, a thin lipid film was obtained. We refer to this sample as the treated powder. To check the phase states of the samples, wide-angle X-ray scattering measurements were performed by an X-ray diffractometer, SmartLab (Rigaku, Japan), at room temperature. The beam source was a copper Kα line (λ = 1.5418 Å), and the scattered beam was collected by a diffractometer with a scan speed of 20°/min and recorded at each 0.01° interval. We confirmed that the diffraction spectra were not changed when the scan speed was set slower than 20 deg/min. Mid-infrared spectra were obtained with an attenuated total reflectionFourier transform infrared (ATR-FTIR) spectrometer (FT/IR6100, JASCO, Japan) at room temperature equipped with an ATR unit where a ZnSe prism was used. The spectral resolution was set to be 0.4 cm−1. For the THz measurements, each lipid sample was finely grained and compressed into a hole of a sample cell with 9 MPa pressure for 10 s. The compressed sample was then under a vacuum for 12 h to remove excess hydrating water. We call this sample the dehydrated sample. The sample hydration was performed by incubating the samples into a container which was humidified by Milli-Q water. The hydration levels were controlled by changing the incubation time. The degree of hydration is represented by a value of R, which is equal to the number of water molecules per one molecule of the lipid. We used averaged R values before and after measurement. In order to estimate the value of R in dehydrated states, the dehydrated sample was first incubated at 95 °C under a vacuum for 2 h, and the difference in the weight of the sample before and after the incubation was measured, which is regarded as the amount of

Figure 1. Chemical structural formulas of (A) DMPC and (B) DMPG.

and the gel phase of DMPG; therefore, it is interesting to investigate the THz spectra in light of polymorphism of the lipid bilayer structures. The hydration degree of the samples is controlled to observe the hydration effect on the THz spectra. The temperature dependence of the THz spectra is studied to monitor the thermal effect on the absorption bands. The complex dielectric spectra are analyzed to determine the peak wavenumbers of the absorption bands. We also performed the same spectral analysis for the complex dielectric spectra of DMPC20 to make a comparison with the DMPG. On the basis of the spectral analyses, we discuss the relationship between the structural properties of the lipid bilayers and the THz absorption spectra.

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EXPERIMENTAL SECTION DMPG and DMPC were purchased from Avanti Polar Lipids, Inc. (Alabaster, Alabama). Other chemicals were purchased from Wako Pure Chemical Industries, Ltd. (Japan). We prepared two different DMPG samples; one is the crystalline phase, and the other is the gel phase. X-ray diffraction experiments showed that the as-received powder was in the

Figure 2. (A) X-ray diffraction patterns of the DMPG bilayer in the crystalline phase (upper) and in the gel phase (lower), respectively, at spacing values from 0.35 to 0.47 nm. (B) X-ray diffraction patterns of the DMPG bilayer and the DMPC bilayer at spacing values from 0.35 to 3.5 nm. B



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−20 °C for longer than 1 week before the experiments, while the treated powder was obtained by dissolving the as-received powder in a mixture of chloroform−methanol and stored at 20 °C after evaporating the solvent. Thus, we conclude that the asreceived powder is in the crystalline phase and the treated powder is in the gel phase. In the crystalline phase, the lipid chains align regularly with specific orientations, while in the gel phase each lipid molecule can rotate more freely with respect to the lipid long axis than in the crystalline phase. Upon hydration of the samples, the X-ray diffraction patterns undergo changes; in both the cases of the crystalline phase and the gel phase, the relative intensity of the diffraction peak at around d = 0.41 nm apparently increases. However, since the position of each diffraction peak does not shift upon hydration, the changes in the diffraction pattern does not indicate any phase transition or drastic structural change; rather than that, regularity along one crystal axis may increase upon hydration in both of the samples. In contrast to DMPG, we previously observed a clear change in the X-ray diffraction pattern of DMPC upon hydration;20 two peaks at 0.41 and 0.425 nm were shifted to 0.415 and 0.43 nm, respectively. It was proposed that these changes correspond to the reconfiguration of the lipid packing, not the phase transition.24 We also performed X-ray diffraction measurements in the spacing range up to 3.5 nm. The results are shown in Figure 2B. We did not obtain diffraction patterns above 3.5 nm because of the serious scattering from the samples. In each sample, observed diffraction patterns are assigned to be caused by the lamellar spacing. For example, in the case of the dehydrated state of the crystalline phase of the DMPG bilayer, diffraction peaks observed at around 2.25 and 1.5 nm are assigned as higher order diffraction of a peak at 4.5 nm. Before and after hydration, the peak positions do not change, showing that no phase transition occurs upon hydration. Similarly, in the case of the gel phase of the DMPG bilayer, diffraction peaks observed at around 2.25 and 1.5 nm are assigned as higher order diffraction of a peak at 4.5 nm. Upon hydration, the peak positions shift toward larger spacing by about 0.05 nm, indicating that the lamellar spacing is slightly expanded upon hydration. However, because the peak shift is not so large, it is concluded that the gel phase structure does not change upon hydration. In the case of the gel phase of the DMPC bilayer, diffraction peaks observed at around 2.7, 1.8, and 1.35 nm are assigned to higher order diffraction of a peak at 5.4 nm. Before and after hydration, the peak positions do not change, representing that no phase transition or no large-scale structural change is induced upon hydration. Previously, it was reported that the DMPC bilayer retained different kinds of gel-phase structures as well as a rippled phase at 25 °C depending on different degrees of humidity.26 Thus, it is possible that the structure of the DMPC bilayer changes upon hydration. Indeed, the diffraction pattern in the range from 0.35 to 0.47 nm changes upon hydration.20 In contrast to this, the diffraction patterns originating from the lamellar spacing are not affected at all, as shown in Figure 2B. These results indicate that, though a slight structural change is induced upon hydration, the structure of the gel phase is unchanged. There are some other diffraction patterns observed at the spacing values between 0.5 and 1.0 nm, as shown in Figure 2B. These peaks may be assigned as those originating from lamellar

hydrating water in the dehydrated state. Temperature was controlled from 123 to 293 K using a cryostat, OptostatDN (Oxford Instruments), operating with liquid nitrogen. Details of the THz-TDS apparatus have been reported elsewhere.22 Briefly, a mode-locked Ti:sapphire laser centered at 800 nm with a pulse duration of 10 fs and a repetition rate of 78 MHz pumped a pair of photoconductive switches that were used as a THz emitter and a detector. A computer-controlled delay was used to detect the temporal waveform of the THz wave. The whole system was placed in a chamber under a flow of dry air. The time-domain detection technique allows us to obtain changes in both the amplitude and phase of the THz wave. By monitoring changes in these quantities with and without a sample, the absorption coefficient (α(ν̃)) and the reflective index (n(ν̃)) (ν̃: wavenumber) can be obtained by Fourier transformation of the THz wave.23 The resultant spectra contain information on dynamics whose time-scale ranges from sub-picosecond to picosecond. The absorption coefficient is described as follows:16 α(ν)̃ =

πν(1 ̃ − e−βhcν)̃ I(ν)̃ 3ε0hcn(ν)̃ V

(1)

where ∞

I(ν̃) =

∫−∞ dt e−i2πcνt̃ ⟨M(0)·M(t )⟩

(2)

I(ν̃) is the line shape function defined as the Fourier transform of the time-correlation function (TCF) of the total dipole moment of the system, ⟨M(0)·M(t)⟩. Other symbols in eq 1 have the usual meanings. The complex dielectric constant ε(ν̃) can be expressed by κ(ν̃) (=ln10α(ν̃)/4πν̃) and n(ν̃) as follows: ε′(ν)̃ = n2(ν)̃ − κ 2(ν)̃ ε″(ν)̃ = 2n(ν)̃ ·κ(ν)̃

(3)

Procedures for the spectral analysis of the complex dielectric spectra are described later.

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RESULTS Structural Characterization by X-ray Diffraction. Figure 2A shows X-ray diffraction patterns of the as-received (upper) and the treated (lower) powders in the region 0.35 nm < d < 0.47 nm where the parameter d is the Bragg spacing. Diffraction patterns in this region have information on the particular lattice and packing density of lipids, and thus, structural information on the lipid bilayers can be obtained by the analysis of the diffraction pattern.24 In the dehydrated state, the diffraction pattern of the as-received powder is obviously different from that of the treated powder, showing that these two samples have different lipid bilayer structures. In the case of the as-received powder, the diffraction peaks can be seen at around d = 0.44, 0.41, 0.40, and 0.38 nm. This diffraction pattern is similar to that of the orthorhombic structure of the crystalline phase as reported previously.25 In contrast to this observation, the diffraction pattern of the treated powder in the dehydrated state (R = 3.4) shows one broad peak centered at d = 0.41 nm with shoulders at around d = 0.44 and 0.39 nm. This diffraction pattern resembles that of the gel phase bilayer.25 It is known that, when DMPG powder in a gel phase is incubated at 4 °C for several days, it is transformed into a crystalline phase. In our case, similarly, the as-received powder had been stored at C



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molecules or a more polar environment around the carbonyl groups. Upon hydration, the spectral shape of this band does not change similarly to the crystalline phase case. By increasing the R value from 3.4 to 4.7, the microscopic environment around the carbonyl groups is not affected. For comparison, the carbonyl stretching modes of the DMPC bilayer in the gel phase are also shown in Figure 3. In the dehydrated state, one peak is observed at 1739 cm−1, while the peak shifts to 1742 cm−1 and one shoulder appears at around 1716 cm−1 concomitantly with hydration. Probably these two components correspond to the two carbonyl groups in DMPC. The hydration dependence is different from the DMPG bilayer cases. One band seems to be blue-shifted, and the other red-shifted. This may indicate that upon hydration the local environment around the carbonyl groups is changed such as hydrogen bond formation or breaking by additional hydrating water molecules. Temperature and Hydration Dependence of THz Spectra of DMPG Bilayers. Figures 4 and 5 show THz

spacing or some lateral lipid packing patterns. The assignment of these peaks remains as a future issue. Mid-Infrared Spectra. In the mid-infrared region, several localized vibrational motions that are sensitive to lipid bilayer structures are observed.25 In Figure 3, we show the absorption

Figure 3. Mid-infrared spectra of the carbonyl stretching region.

spectra and their second derivative spectra. Figure 3 shows a spectral region corresponding to vibrational modes originating from two carbonyl stretching bands of DMPG bilayers. The vibrational modes often contain information about hydrogen bonding and the polarity of the surrounding environment.25 Generally, the carbonyl stretching mode is red-shifted when it forms a hydrogen bond with protic molecules or when its environment becomes polar. In the case of the crystalline phase, one absorption band is observed at 1731 cm−1 with a shoulder at around 1747 cm−1. Probably these two components correspond to the two carbonyl groups, though we cannot assign the bands completely at present. Upon hydration, the spectral shape remains similar, indicating that the microscopic environment around the carbonyl groups, such as the number of the hydrogen bonding water molecules and/or polarity around the carbonyl groups, does not change even though the hydration amount is increased. Thus, when the value of R is increased from 1.3 to 2.1 by hydration, hydrating water molecules go not to the carbonyl groups in DMPG but to other polar groups such as the two hydroxyl groups or the phosphate group. In the gel phase, one absorption band at 1739 cm−1 and a shoulder at around 1724 cm−1 are observed. Similar to the crystalline phase case, there are two components in this band, probably corresponding to the two carbonyl groups in DMPG. This band is red-shifted compared with that in the crystalline phase. This may be due to the fact that the R value is larger in the gel phase, providing more hydrogen bonding water

Figure 4. Temperature-dependent THz spectra of the DMPG bilayer in the crystalline phase.

absorption spectra of DMPG of the crystalline phase and the gel phase, respectively. In the crystalline phase, two absorption bands are observed at around 36 and 70 cm−1. In the gel phase, similarly, two absorption bands whose bandwidth is larger than that in the crystalline phase are observed at around 40 and 60 cm−1. Such absorption bands have been observed in molecular crystals27−31 as well as polymers32 and polypeptides33,34 in the solid state. In addition to these absorption bands, a monotonic increase in the absorption coefficients can be seen as the wavenumber increases. Such background components have often been observed in the absorption spectra of other biomolecules such as proteins33,35,36 and can be considered as the sum of a large number of absorption bands distributed in D



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main absorption bands at 36 and 70 cm−1 are labeled as VR=1.3 2 and VR=1.3 , respectively. One small band at around 25 cm−1, 4 VR=1.3 , is also needed to obtain better fitting results of the 1 spectra. The spectral component of VR=1.3 is regarded as a 5 background that may represent a sum of the absorption bands. The complex dielectric spectra of the hydrated states of the DMPG bilayer in the crystalline phase can be fitted with eq 4 with n = 5, as shown in Figure 6A (123 K). In the hydrated states, an additional component, VR=2.6 or VR=3.0 , is needed at 3 3 −1 around 41 cm . To see the temperature and hydration dependence of the absorption bands, the peak wavenumbers of the two main absorption bands at 36 and 70 cm−1 obtained by the fitting are plotted as a function of temperature in parts B and C of Figure 6, respectively. The peak wavenumber of the component at 36 cm−1 is almost independent of temperature, while that at 70 cm−1 is red-shifted as temperature increases. Next we show the results for the gel phase of DMPG. The results of the dehydrated and hydrated states at 123 K are shown in Figure 7A. In every hydration degree, the spectra are fitted fairly well with eq 4 with n = 4. The two main absorption bands at 40 and 60 cm−1 are referred to as VR=X and VR=X 2 3 , respectively, where X denotes the hydration degrees of 3.4, 4.8, or 5.5. One broad component in the lower wavenumber region, VR=X 1 , is needed to obtain better results. The last component, VR=X (X = 3.4, 4.8, or 5.5), is considered as a sum of the 4 absorption bands similarly to the crystalline phase case. The peak wavenumbers of the main absorption bands at 40 and 60 cm−1 obtained by the fitting are plotted as a function of temperature and hydration amount, shown in Figure 7B and C, respectively. No obvious hydration dependence is observed at each temperature investigated. While the absorption band at 40 cm−1 rarely shifts within experimental error, the absorption band found at 60 cm−1 is red-shifted as temperature increases. Finally, we show the fitting results for the gel phase of DMPC at 123 K in Figure 8. In the dehydrated state, the spectra are fitted well by eq 4 with n = 2, as shown in Figure 8A at 123 K. There is a peak at 42 cm−1, named VR=3.5 . VR=3.5 1 2 represents a broad background component. In contrast to this, three underdamped modes are needed to reproduce the spectra of the hydrated states (Figure 8A). Furthermore, in the high temperature region (>220 K), the spectral intensity of the imaginary part increases in a frequency region below 20 cm−1, as shown in Figure 8B (293 K). We find that the complex dielectric spectra can be reproduced well if we add one Debye relaxation mode to the model function

Figure 5. Temperature-dependent THz spectra of the DMPG bilayer in the gel phase.

the THz region. The spectral intensities increase with temperature increase nearly linearly in both the dehydrated and hydrated states. This is in contrast to the DMPC bilayer case where we observed apparent inflection points in the increase of the absorption coefficients at around 240 K only in the hydrated states of the bilayer.20 We concluded that the inflection points are related to thermal activation of hydrating water dynamics. The inflection point may be due to an onset of a relaxation mode due to hydrating water, which will be discussed later. Hereafter, we focus on the absorption bands and not the background components. Spectral Analysis of the Complex Dielectric Spectra. To make a quantitative discussion on the absorption bands, especially on the center wavenumbers of the bands, we perform spectral analysis phenomenologically; the real and imaginary parts of the complex dielectric spectra are simultaneously fitted with a model function. We find that a sum of underdamped modes is a proper model function to represent the complex dielectric spectra n

ε*(ν)̃ =

∑ j=1

Aj 2

2

νj̃ − ν ̃ − iνγ̃ j

n

ε*(ν)̃ =

∑ j=1

Aj 2

2

νj̃ − ν ̃ − iνγ̃ j

+

εDebye 1 − 2πicντ̃ Debye

+ εinf (5)

where εDebye and τDebye denote the dielectric strength and the relaxation time of the Debye relaxation mode, respectively. The fitting results at 293 K are shown in Figure 8B. The main absorption peak at 30 cm−1 is referred to as VR=X (X = 6.8 or 1 7.9). The spectral components of VR=X and VR=X (X = 6.8 or 2 3 7.9) represent background components. The peak wavenumber of the main absorption band, VR=X (X = 3.5, 6.8, or 7.9), at each 1 hydration level is plotted as a function of temperature in Figure 8C. The peak wavenumber of the absorption band in the hydrated states does not change as the temperature increases, while that in the dehydrated state is red-shifted. The temperature dependence of the dielectric strength εDebye and the relaxation time τDebye of the Debye relaxation mode are

+ εinf (4)

where Aj, ν̃j, and γj represent the amplitude, the center wavenumber, and the damping constant of a vibrational mode, respectively. εinf represents the constant in the high frequency limit. i represents the imaginary unit. The number of the vibrational modes n is determined so that the absorption bands are appropriately fitted. In Figure 6A, we show the fitting results for the crystalline state of DMPG at 123 K. In the dehydrated state, the complex dielectric spectra can be fitted by four underdamped modes. We refer to each mode as VR=X (j = 1, 2, j 4, and 5), where X represents the hydration degree. The two E



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Figure 6. Simulation results of the complex dielectric spectra of the DMPG bilayer in the crystalline phase. (A) The upper and lower panels show the real and imaginary parts, respectively, at 123 K. In each figure, the simulation results obtained by using eq 4 are shown by black lines, while the experimental results are shown by gray circles. In the imaginary part, the spectral components obtained by the fitting are displayed. (B and C) The peak positions and bandwidth of the absorption bands at around 36 cm−1 (B) and 70 cm−1 (C) in the dehydrated and hydrated states are plotted as a function of temperature. The curves in part C are the simulation results by using eq 7.

DMPC bilayer in the gel phase is clearly changed. The midinfrared spectra of the carbonyl stretching modes also show insensitivity to hydration for DMPG. The two lipid bilayers DMPC and DMPG differ in their chemical structure; DMPC is zwitter ionic, and DMPG is anionic with sodium cation as a countercation. Because of the electrical property difference, the number of hydrating water molecules differs for the two lipid bilayers. For the DMPG bilayer, the R value of the wellhydrated state is 5.5, while the hydration amount of the DMPC bilayer can go up to R = 7.9. The X-ray diffraction indicates that the packing pattern of the lipid molecules in the DMPC bilayers is changed by hydration water, while those of the DMPG bilayers do not change. Similarly, the peak wavenumbers of the THz absorption bands of the DMPC bilayer largely change, while those of the DMPG remain unchanged before and after hydration. These results show that the THz absorption bands are sensitive to the

shown in Figure 8D. The relaxation time is in the subpicosecond time scale for all of the temperatures. Tielrooij et al. studied dielectric relaxation dynamics of water in 1,2-dioleoylsn-glycero-3-phosphocholine lipids (DOPC) by THz spectroscopy.17 They found very rapidly reorienting water molecules whose relaxation time is in the sub-picosecond range. The time scale and dielectric strength of this fast component are similar to the present results for DMPC. Therefore, it is suggested that in the hydrated DMPC there are fast reorienting water molecules similar to the DOPC case.

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DISCUSSION Effect of Hydration on Lipid Bilayer Structures. First, we briefly discuss the relationships between hydration and the structural changes of the lipid bilayers. As shown by the X-ray diffraction experiments, upon hydration, the lipid packing patterns of the DMPG bilayers do not change, while that of the F



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Figure 7. Simulation results of the complex dielectric spectra of the DMPG bilayer in the gel phase. (A) The upper and lower panels show the real and imaginary parts, respectively, at 123 K. In each figure, the simulation results obtained by using eq 4 are shown by black lines while the experimental results are shown by gray circles. In the imaginary part, the spectral components obtained by the fitting are displayed. (B and C) The peak positions of the absorption bands at around 40 cm−1 (B) and 60 cm−1 (C) in the dehydrated and hydrated states are plotted as a function of temperature. The curves in part C are the simulation results by using eq 7.

VR=X (X = 1.3, 2.6, or 3.0) in the DMPG bilayer in the 2 crystalline phase at every hydration degree is a typical example of such absorption bands; the peak wavenumber of the absorption band remains almost unchanged at around 36 cm−1 throughout the experimental temperature range (Figure 6B, upper). However, its bandwidth gradually increases with temperature increase (Figure 6B, lower). To quantitatively evaluate the degree of anharmonicity, the temperature dependence of the peak wavenumbers of the absorption bands is fitted by the following empirical equation:29,38

conformational states of the lipid packing patterns in the bilayers. It has often been said that the low-frequency vibrations of a molecular crystal are intermolecular vibrations, or phonons. On the other hand, recent THz spectroscopic studies combined with quantum chemical calculations have shown that there are contributions from both the inter- and intramolecular modes to the low-frequency vibrational bands. Zhang et al. developed a computational method to calculate relative contributions of the translational intermolecular mode, librational mode, and intramolecular mode to the normal mode in the low-frequency vibration.37 They found that for a rigid molecule like adenine the THz absorption bands below 100 cm−1 are mostly contributed by the intermolecular vibrations. On the other hand, for a flexible molecule like adenosine, the intramolecular and intermolecular vibrations are highly mixed even in the lowfrequency regions. From these results, we suggest that the lowfrequency bands observed in the lipid bilayers have characteristics of the inter- and intramolecular vibrations, since the lipid molecules have a number of single covalent bonds which allow many intramolecular rotational motions. Anharmonicity of the Absorption Bands. Several absorption bands show a red shift with increasing temperature. For example, VR=1.3 or VR=2.6 of the DMPG bilayer in the 4 4 crystalline phase shifts to the lower frequency region with an increase in their bandwidth (Figure 6C). On the other hand, several absorption bands do not show peak shifts. For example,

ν(̃ T ) = ν0̃ −

ATc exp(Tc/T ) − 1

(6)

where ν̃0, A, and Tc represent the center wavenumber at 0 K, a constant related to anharmonicity of the vibrational potential, and the characteristic temperature related to the energy of the effective phonon, respectively. This function exhibits a monotonic decrease with an inflection point at around Tc/3. Far above Tc, the function becomes linear by approximating the exponential with the first order of the Taylor series as follows: ν(̃ T ) = ν0̃ − AT

(7)

We fitted several temperature dependencies of the peak wavenumbers, as shown in Figures 6C, 7C, and 8C. The fitting results are shown in Table 1. The fact that each plot can G



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Figure 8. Simulation results of the complex dielectric spectra of the DMPC bilayer in the gel phase. (A and B) The upper and lower panels show the real and imaginary parts, respectively, for 123 K (A) and 293 K (B). In each figure, the simulation results obtained by using eq 4 or 5 are shown by black curves, while the experimental results are shown by gray circles. In the imaginary part, the spectral components obtained by the fitting are displayed. (C) The peak positions of several absorption bands in the dehydrated and hydrated states are plotted as a function of temperature. The curve in part C indicates the simulation results by using eq 7. (D) Parameters obtained by the spectral analysis by using the Debye relaxation function, eq 5. Upper and lower panels show the amplitude and the relaxation time, respectively. The inset in the lower panel shows all the data points for the relaxation time including that at 220 K, which is deviated from the others.

Table 1. Fitting Results of the Temperature Dependence of the Peak Wavenumbers of the Absorption Bands Obtained by eq 6 DMPG, crystalline phase −1

ν̃0 (cm ) A (cm−1/K)

DMPG, gel phase

DMPC, gel phase

VR=1.3 4

VR=2.6 4

VR=3.4 3

VR=4.8 3

VR=5.5 3

VR=3.5 1

73 ± 1 0.020 ± 0.005

74 ± 1 0.025 ± 0.007

65 ± 2 0.026 ± 0.010

65 ± 1 0.025 ± 0.007

65 ± 2 0.024 ± 0.010

52 ± 3 0.043 ± 0.012

H



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be fitted by the linear function represents that the value of Tc is much lower than the lowest temperature in this experiment, i.e., 123 K. It is seen that in the cases of the DMPG bilayers the values of ν̃0 and A are similar before and after hydration within the experimental error, indicating that the vibrational potentials of the low-frequency modes are not affected upon hydration. On the other hand, no clear relationship is observed between the bilayer structures and anharmonicity. Linfield and co-workers observed the temperature dependence of the THz absorption spectra of several molecular crystals such as purine and adenosine.29,38 They analyzed the temperature dependence of the absorption bands in terms of eq 6, and most of the values of A are in the region from 0.007 to 0.023 cm−1/K. For the DMPG crystalline phase, the value of A is similar to these values. However, the A values of the gel phases of DMPC and DMPG are somewhat larger than those of the molecular crystals. Therefore, it is suggested that the lowfrequency vibrational modes of the gel phase lipid bilayers are slightly more anharmonic than those of the molecular crystals, probably due to larger degrees of freedom of rotational and translational motions in gel phases. Detailed theoretical modeling and calculations will help us to understand the vibrational modes in the low-frequency region fully.

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SUMMARY We investigated the temperature and hydration dependence of the THz spectra of DMPG in the crystalline and gel phases by THz-TDS and compared the results with those of the DMPC bilayer in the gel phase that we previously reported. It was shown that different spectral patterns were observed in the three cases in the dehydrated state. However, upon hydration, the spectra of the DMPG bilayers were not affected, while a drastic spectral change was observed in the case of the DMPC bilayer. These different sensitivities to hydration were consistent with the results of the X-ray diffraction patterns and the mid-infrared spectra of the carbonyl stretching modes, indicating that the THz absorption band structures reflect the lipid packing patterns. The bandwidth of the absorption bands in the crystalline phase was always narrower than that in the gel phase, representing that the bandwidth can be used to distinguish different lipid bilayer phases where the crystallinity of lipid packing patterns is different. In contrast to this, no correlation was observed between the anharmonicity of the absorption bands estimated from temperature dependence and structural properties such as lipid bilayer phases and hydrating states.

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AUTHOR INFORMATION

Corresponding Author

*Phone and Fax: +81-78-803-5684. E-mail: tominaga@kobe-u. ac.jp. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is partially supported by Industry-Academia Collaborative R & D from Japan Science and Technology (JST).

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REFERENCES

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Temperature and Hydration Dependence of Low-Frequency Spectra

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