Dynamical behavior of hydration water molecules between

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Dynamical Behavior of Hydrated Water Molecules Between Phospholipid Membranes Takeshi Yamada, Nobuaki Takahashi, Taiki Tominaga, Shin-ichi Takata, and Hideki Seto J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01276 • Publication Date (Web): 08 Aug 2017 Downloaded from http://pubs.acs.org on August 13, 2017

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The Journal of Physical Chemistry

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Dynamical behavior of hydration water molecules between phospholipid membranes Takeshi Yamada*†, Nobuaki Takahashi‡, Taiki Tominaga†, Shin-ichi Takata§, Hideki Setoǁ †

Neutron Science and Technology Center, Comprehensive Research Organization for Science

and Society (CROSS), Tokai, Naka, Ibaraki, Japan 319-1106 ‡

Institute for Chemical Research, Kyoto University Gokasho, Uji, Kyoto, Japan 611-0011.

§

J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirakata, Tokai Japan 319-1195.

ǁ

J-PARC Center, High Energy Accelerator Research Organization, 203-1 Shirakata, Tokai,

Ibaraki, Japan 319-1106. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] KEYWORDS 1,2-dimyristyl-sn-glycero-3-phosphocholine (DMPC), quasi-elastic neutron scattering, water, hydration, phospholipid membrane, dynamics

ACS Paragon Plus Environment

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Table of Contents


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ABSTRACT The dynamical behavior of hydration water sandwiched between 1,2-dimyristylsn-glycero-3-phosphocholine (DMPC) bilayers was investigated by quasi-elastic neutron scattering (QENS) in the range between 275 and 316 K, where the main transition temperature of DMPC is interposed. The results revealed that the hydration water could be categorized into three types of water: (1) free water, whose dynamical behavior is slightly different from that of bulk water; (2) loosely bound water, whose dynamical behavior is one order of magnitude slower than that of the free water; and (3) tightly bound water, whose dynamical behavior is comparable with that of DMPC molecules. The number of loosely bound and tightly bound water molecules per DMPC molecule monotonically decreased and increased with decreasing temperature, respectively, and the sum of these water molecules remained constant. The number of free water molecules per DMPC molecule was constant in the measured temperature range.


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I.

Introduction

Biological molecules such as nucleic acids, proteins, and carbohydrates are surrounded by water molecules and their biological functions can only be realized in relation with water. Thus, the importance of elucidating the structure and dynamics of water molecules near biological molecules is widely recognized. Several experimental and computational studies have been conducted on water molecules near lipid membranes so far. Marrink et al. reported that the hydration force and the dynamics of water molecules between lipid bilayers depend on the water structure by molecular dynamics simulations [1]. Zhao et al. investigated the dynamics of water at the surface of a stack of multilamellar bilayers of phospholipid 1,2-dilauroyl-sn-glycero-3phosphocholine (DLPC) using ultrafast polarization selective vibrational pump–probe spectroscopy [2], and showed that the water molecules near lipids are distinct from hydration water at the phosphate and choline groups. The relaxation time for the structural rearrangement of water molecules decreased with increasing amounts of water. Kundu et al. used femtosecond mid-IR pump−probe spectroscopy to show that the structure and dynamics of water between 1,2dimyristyl-sn-glycero-3-phosphocholine (DMPC) bilayers changed as the DMPC bilayer changed structure from the gel phase to the liquid crystalline phase [3]. This pump–probe spectroscopy technique observes water molecules closest to the head group of the phospholipid. Hishida and Tanaka investigated the dynamics of water in an aqueous DMPC solution by THz spectroscopy and showed that 28 water molecules were hydrated per DMPC molecule, which was larger than the value previously reported [4]. Choi et al. used THz spectroscopy to determine that the hydration water to total water ratio of DMPC increased at the transition from the gel phase to the liquid crystalline phase [5]. The THz spectroscopy technique is sensitive to water dynamics occurring on the picosecond time scale, such as reorientation of water molecules.


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Quasi-elastic neutron scattering (QENS), covering both the picosecond to nanosecond time scale, and the 10-2 to 101 nanometer length scale, is an appropriate method for investigating the dynamics of both hydration water and bulk water. Additionally, it is possible to observe the selfcorrelated dynamics of a specific component of complex systems in combination with selective deuteration, such as in lipid/water systems [6-11] and protein/water systems [12], because hydrogen has a larger incoherent scattering cross section than that of deuterium and other elements. Köenig et al. measured the dynamical behavior of water molecules in oriented perdeuterated 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (d75-DPPC) bilayers by QENS and NMR [6], and showed that water molecules exhibited a rotational motion in the low hydration state and a translational motion in the high hydration state. In their experimental results, the dynamical behavior was homogeneous and anisotropy was not observed. Toppozini et al. recently investigated the dynamical behavior of water molecules between DMPC bilayers deposited on silicon wafers [8]. They showed heterogeneous dynamics that depended on the orientation of the bilayer planes. However, they used a partially deuterated lipid, d54DMPC25H2O. In this case, the QENS signal from hydrogen in the trimethyl group of DMPC could not be ignored because its contribution to the QENS signal was ~20%. Swenson et al. addressed this problem by subtracting the QENS signal of d54DMPC-9D2O from that of d54DMPC-9H2O [9]. Using a perdeuterated lipid whose hydrophilic head group is deuterated is another approach that would reduce the incoherent scattering from lipid molecules, as reported by König et al. [6]. However, the dynamics of hydration water in the sub-nanosecond time scale have not been clarified. Based on these experimental results, we investigated the dynamical behavior of water molecules between DMPC bilayers by QENS with a high-energy resolution (EReso = 3.6 µeV)


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and a wide energy transfer (∆E) range (−0.5 ≤ ∆E / meV ≤ 0.5). These experimental conditions allow determination of the dynamics of both hydration water and free water, using selective deuterated samples (d67DMPC-37H2O and DMPC-35D2O). This paper is constructed as follows, (1) the structure and phase transition temperature of the sample were verified. (2) The QENS profiles of d67DMPC/H2O were analyzed in terms of three modes that cover a wide relaxation time range: tightly bound water, loosely bound water, and free water. The relation on dynamics between water and DMPC molecules was discussed. (3) The numbers of each type of water molecule and the temperature dependence were estimated. Finally, the effect of phase transitions of DMPC molecule on the numbers of each type of water was discussed. II.

Samples and Experiments

The perdeuterated lipid d67DMPC was purchased from Avanti Polar Lipids Inc.; its isotopic purity was > 99% and it was used without further purification. The fractions of the incoherent scattering cross sections from d67DMPC and 37 H2O are 8% and 92%, respectively. The d67DMPC was dried at room temperature with a turbo molecular pump overnight. The d67DMPC powder (100 mg) was mixed with an appropriate amount of water to give a ratio of 37 water molecules per DMPC molecule (denoted as d67DMPC-37H2O) corresponding to almost the maximum water amount incorporated between lipid bilayers [4]. The solution was made in a glove box under conditions of 100% relative humidity under a helium atmosphere. The mixture was wrapped with aluminum foil (~90 mm width × ~30 mm height), placed in an aluminum cylinder cell (outer and inner diameters of 14.5 and 14.0 mm, respectively), and sealed with a stainless steel (SUS321TB) O-ring. A mixture of protonated DMPC and 35 D2O molecules per lipid molecule (DMPC-35D2O) was also prepared to observe the dynamics of the DMPC


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molecules. The fractions of the incoherent scattering cross sections from DMPC and D2O are 98% and 2%, respectively. The compositions were determined by a gravimetric method. The QENS measurements were carried out using a time-of-flight near backscattering spectrometer DNA [13, 20] at the Materials and Life Science Experimental Facility (MLF) in the Japan Proton Accelerator Research Complex (J-PARC) in Tokai, Japan. The injected proton beam power incident on the neutron target was ~300 kW. The energy resolution was 3.6 µeV using a Si 111 analyzer. The covered Q range was between 0.07 and 1.86 Å-1. The elastic intensity scan was performed between 50 and 300 K with heating at 1 K min-1. The QENS measurements of d67DMPC-37H2O were performed at 316, 305, 295, 285, and 275 K using three different fast chopper phase settings whose energy transfer (∆E) range was −0.5 ≤ ∆E / meV ≤ 0.5. The exposure time for each QENS measurement was ~11.5 hours. The instrumental resolution was measured at 50 K. The QENS measurement of DMPC-35D2O was also carried out at 306 K and -0.04 < ∆E / meV < 0.1. Small-angle neutron scattering (SANS) experiments were carried out at TAIKAN at MLF, JPARC [26]. The sample DMPC-35D2O was prepared by the same procedure as that used for the QENS experiments. For the SANS measurement, the sample was mounted on a sample cell, which was a flat type cell with quartz windows and a titanium spacer, sealed by back-up o-rings and tightening retainers on each side. The spacer thickness was 1 mm. The irradiated beam size was 10 mm diameter. The measured temperature was 308 K. The measured Q range was 0.007 < Q / Å-1 < 1.0.


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III.

Results and Discussion

Figure 1. SANS profile of DMPC-35D2O at 308 K. Figure 1 shows a SANS profile of DMPC-35D2O at 308 K in the liquid crystalline phase. The three Bragg peaks are clearly observed at 0.116, 0.232, and 0.349 Å-1, indicating the lamellar structure. The lamellar repeat distance was 54.2 Å, which corresponds to the lamellar structure at 99% relative humidity [27]. Each Bragg peak is sharp enough (~5%, which is comparable with the instrumental resolution) to show that water molecules are incorporated between lipid bilayers and all the irradiated sample regions have the same lamellar structure. This means that we could prepare homogeneous multilamellar vesicles by the sample preparation procedure described in the Samples and Experiments. Note that the size distribution of the multilamellar vesicles in micrometer scale exist, however, it affects neither the SANS profiles nor QENS signals because these experiments reveal the structure and dynamics in the sub-nanometer scale.


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Figure 2. Elastic intensities of d67DMPC-37H2O at Q = 0.15 (circle), 0.60 (square) and 1.60 Å-1 (triangle). Figure 2 shows the elastic scattering intensities from d67DMPC-37H2O at Q = 0.15 (circle), 0.60 (square) and 1.60 Å-1 (triangle). If the thermal motions of molecules are represented by a harmonic oscillator, the temperature dependence should be linear. That is, any deviation from a straight line indicates the possibility of relaxation and/or anharmonic oscillation in the sample. The elastic intensities at Q = 0.60 and 1.6 Å-1 decrease drastically at 273 K, the melting point of bulk water (Tw). This result indicates that a part of the incorporated water is freezable water, which is consistent with previous differential scanning calorimetry (DSC) results [14]. No jump of the elastic intensity is observed at Q = 0.15 Å-1 at 273 K, due to the strong coherent scattering from the stack of lipid bilayers. Incoherent scattering is a major contribution to the neutron scattering intensity of the d67DMPC-37H2O (88% of the total scattering cross section), while coherent scattering is superimposed at Q = 0.15 and 1.60 Å-1 because of the lamellar structure


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and the correlation of alky chains [21], respectively. Changes in the coherent elastic intensity reflect not only the possibility of relaxation, but also the possibility for structural change in the sample. The elastic intensity at Q = 0.15 Å-1 changes at 281 and 293 K. These changes correspond to the pre-transition temperature of the lipid, Tpre (from the gel phase to the ripple-gel phase), and the main transition temperature, Ttr (from the ripple-gel phase to the liquid crystalline phase), respectively [18], because the coherent scattering intensity changes with structural changes of the lipid bilayers. The change in the elastic intensity at Q = 1.60 Å-1 at 293 K also corresponds to the main transition temperature where the alkyl chains of lipids melt. The coherent elastic scattering from the alkyl chains in the solid-state changes into QENS in the molten state at Ttr. Otherwise, no conformational change in the alkyl chain occurs at the pretransition, and no change in the elastic intensity at Q = 1.60 Å-1 is observed at Tpre. From these results, Tpre and Ttr of the d67DMPC-37H2O were estimated to be 281 and 293 K, respectively, which is slightly lower than the previously reported values for DMPC [18]. This difference might be caused by the deuteration effect, as reported by Guard-Fiar et al. [19].


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Figure 3. QENS profile of DMPC-35D2O at Q = 1.1 Å-1 at 306 K. The diamonds are the experimental data and the bold solid line is the result of fitting to Eq. (1). The dashed-dotted and dotted lines are LTrs and LInt in Eq. (1), respectively.

Figure 3 shows the QENS profile of DMPC-35D2O at 1.1 Å-1 and 306 K. Since most of the incoherent scattering intensity (98%) from this sample is incoherent scattering from hydrogen atoms in DMPC molecules, the QENS signals could be regarded as reflections of the dynamical motion of lipid molecules. The QENS profile is fitted well by Eq. (1) [7], which includes both the translational mode corresponding to the lateral diffusion of the DMPC in the bilayer membrane, and the internal mode of the DMPC: S (Q , E ) = {ATrs LTrs ( Γ Trs , E ) + AInt LInt ((ΓTrs + ΓInt ), E )} ⊗ R (Q , E ) + BG

(1)

where L, A, Γ, R, BG and ⊗ are Lorentz function, the coefficient of the Lorentz function, halfwidth at half-maximum of the Lorentz function, a resolution function, a constant background and convoluted integration, respectively. The subscripts “Trs” and “Int” indicate the translational and the internal modes, respectively.


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Figure 4. Half-width at half-maximum values of the translational mode (ΓTrs) of DMPC-35D2O obtained by profile fitting to Eq. (1) at 306 K. The solid line is the result of fitting to Eq. (2).

The Q2 dependence of ΓTrs of DMPC-35D2O is shown in Figure 4. As reported by Sharma et al. [7], the ΓTrs follows Fick’s law (Eq. (2)).

ΓTrs = DTrsQ2

(2)

where DTrs is the diffusion coefficient of a DMPC molecule. The temperature dependence of the diffusion coefficients are shown in Figure 9 and discussed later. The obtained diffusion coefficient of DMPC molecules is consistent with the value in literature for DMPC-35D2O reported by Busch et al. [10] and with the value of DTight for d67DMPC-37H2O at 305 K shown in Figure 9.


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Figure 5. QENS profiles of d67DMPC-37H2O at 0.92 Å-1 and 316 K. The circles are experimental data and the bold solid line is a curve fitted to the data using Eq. (3). The dashed, dashed-dotted and solid lines are LFree and LLoose, LTight in Eq. (3), respectively.

Figure 5 shows the QENS profile of d67DMPC-37H2O at Q = 0.92 Å-1 at 316 K (liquid crystalline phase). Broadening caused by quasi-elastic scattering was observed in the measured energy transfer range. The observed QENS profiles above Ttr (T = 316, 305 and 295 K) are fitted by the sum of three Lorentz functions as follows (Eq. (3)). S ( Q , E ) = {ATight L Tight ( Γ Tight , E ) + ALoose L Loose ( Γ Loose , E ) + AFree L Free ( Γ Free , E )}⊗ R ( Q , E ) + BG (3)

where the subscripts “Tight”, “Loose”, and “Free” indicate the tightly bound water, the loosely bound water, and the free water, respectively, as described below. The fitting result reproduces the experimental data well, as shown in Figure 5. Note that the trial to fit with more Lorentz functions did not improve the quality of the fitting results as shown in Figure S1 (supporting information), and three Lorentz functions (eq. (3)) could be the best candidate to explain the


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results. It is reasonable to consider that the QENS intensity mainly arises from incoherent scattering of the water. Eq. (3) suggests that the dynamics of the water incorporated in lipid bilayers are separated into three different time scales, which could originate from the interactions between the hydrophilic head group of the DMPC and the water. DSC results previously reported by Aoki and Kodama showed that the hydration water in lipid bilayers is separated into bulk, freezable, and non-freezable water, and that the hydration number of DMPC was 10 water molecules per DMPC molecule [14]. Disavlo et al. discussed in their review [15] that the hydration water is separated into tightly bound water and loosely bound water by the strength of its hydrogen bonding to the head group of the phospholipid molecule, and that there were ~6–12 hydration water molecules per DMPC molecule. Toppozini et al. analyzed QENS data using the Kahlarusch-Williams-Watts (KWW) function to describe the heterogeneous dynamics of water in DMPC bilayers and showed the anisotropy of the dynamics [8]. As they discussed, it is difficult to distinguish the validity of the data analysis from the reduced chi-squared values in many cases: the sum of the Lorentz functions or the sum of a delta (elastic) and the Fouriertransformed KWW functions. The fitting of QENS data is also subject to the energy resolution and energy window of the data. Thus, the physical meaning of the models used in each data analysis is critical. Considering previous reports [2, 14, 15] and our results that freezable water, which is similar to bulk water, exists in the DMPC bilayer, and that the slowest dynamics are cooperative with that of DMPC as described below, it is reasonable to separate the dynamics of the water into distinct relaxations. Consequently, the incorporated water corresponding to the three relaxations in Eq. (3) are represented as follows; tightly bound water (Tight), loosely bound water (Loose) and free water (Free) in order from long (narrow Γ) to short (wide Γ) relaxation time.


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Figure 6. Half-width at half-maximum values (Γ) of d67DMPC-37H2O at 316 K obtained by profile fitting to Eq. (3). The circles, squares, and triangles are ΓFree, ΓLoose and ΓTight in Eq. (3), respectively. The solid lines on ΓFree, ΓLoose are fitted results obtained by Eq. (4). The solid line on ΓTight is a fitted result to Eq. (2). The Q dependence of Γ and A reflects the nature of molecular motion such as translational motion and rotational motion. Figure 6 shows the Q2 dependence of Γ for d67DMPC-37H2O at 316 K obtained by profile fitting to Eq. (3). The ΓFree and ΓLoose of the d67DMPC-37H2O follow the jump-diffusion model (Eq. (4)) [16]:

Γ=

DQ 2 1 + DQ 2τ 0

(4)


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where D and τ0 are the diffusion coefficient and the mean residence time, respectively. This result indicates that the free water and the loosely bound water exhibit translational diffusion. The obtained diffusion coefficients are shown in Figure 9. The ΓTight varies proportionally with Q2 (Eq. (2)). As shown in Figure 9, the obtained diffusion coefficient is almost the same as that of the DMPC molecules (DMPC-35D2O). This result indicates that the tightly bound water exhibits cooperative motion with DMPC molecules. As described in Samples and Experiments, 8% contribution of the incoherent scattering from the d67DMPC is small but non-negligible. One method of subtracting the contribution of d67DMPC would be to measure d67DMPC-37D2O and calculate the difference between them {(d67DMPC-37H2O)-(d67DMPC-37D2O)}. However, it should be noted that the contribution of the coherent scattering from D2O is difficult to estimate, and the QENS of the d67DMPC-37D2O was not measured in our experiment. Meanwhile, the tightly bound water exhibits cooperative motion with DMPC molecules as mentioned above. Thus, the contribution of the incoherent scattering from d67DMPC was included in that of the tightly bound water across the measured temperature range, and was taken into consideration in the estimation of the number of the tightly bound water as discussed below. In the data analysis described above, the observed motions are regarded as translational motions. However, the rotational motion of both the hydration water and DMPC molecules also occurs simultaneously, and the contributions should be superimposed on Eq. (3). In general, the rotational motion is faster than the translational motion. This means that the height and width of the Lorentz function due to the rotational motion is lower and wider than those of the translational motion. The contribution of the rotational motion imposes not only on the selfcomponent but also on other faster components, i.e. the contributions from the loosely bound


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water, the free water and the constant background. It is better to express the dynamical behavior of water including both the contributions of the translational and the rotational modes as in the case of bulk water [23], the Eq. (3) should include more Lorentz functions. In this case, the HWHM from the rotational mode is independent of Q. The intensity from the rotational mode follows the sum of primary and higher kinds spherical Bessel functions and approaches to zero at Q = 0. Thus, we have tried to fit the QENS spectra by the function with the fourth Lorentz function, but the fitting result was not improved as show in the supporting information (Figure S1). This means that the analysis with more complex function than the present one (eq. (3)) is difficult. The Q2 dependence of HWHM obtained from our data analysis as shown in Figure 6 and Figure 8 could be interpreted as the translational diffusion. This result supports that the hydration water is separated into three types of water. Since the rotational mode is superimposed on eq. (3) and that of the intensity increases with increasing Q, the mean residence time should be affected. Meanwhile, the diffusion coefficient determined in low Q region is little affected by the rotational mode.


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Figure 7. QENS profiles of d67DMPC-37H2O at 0.92 Å-1 at 285 K. The circles are experimental data and the bold solid line indicates the results after fitting to Eq. (5). The dashed, dashed-dotted and solid lines are LFree and LLoose, δTight in Eq. (5), respectively.

The QENS profiles at 285 K (ripple gel phase), and 275 K (gel phase) are fitted well by Eq. (5), as shown in Figure 7: S ( Q , E ) = {ATight δ Tihgt ( E ) + ALoose L Loose ( Γ Loose , Q ) + AFree L Free ( Γ Free , Q )}⊗ R ( Q , E ) + BG

(5)

Although Sharma et al. analyzed the QENS data in the ripple gel phase with the translational mode by a Lorentz function [7], the tightly bound water is represented by a delta function (δTight) below Ttr (T ≤ 293 K), because ΓTight was much narrower than that of the resolution function. The difference might be due to the ratio of water and lipid molecules (37 H2O per DMPC molecule in our case and 708 D2O per DMPC molecule in Sharma et al.) and/or different forms of the vesicles (multilamellar vesicles in our case and unilamellar vesicles in Sharma et al.). As S. Mitra et al. reported that a lateral motion of a surfactant molecule in a multilamellar vesicle


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(MLV) was slower than that of in the unilamellar vesicle (ULV) and that the immobile fraction of the MLV was more than that of ULV [28], the lateral motion even in the membrane was affected by the vesicle shape. This report supports our model using Eq. (3) and (5) in the liquid crystalline phase and the gel phase, respectively.

Figure 8. Half-width at half-maximum values of (Γ) of d67DMPC-37H2O at 285 K obtained by profile fitting to Eq. (5). The circles and squares are ΓFree, ΓLoose, respectively. The solid lines of

ΓFree, ΓLoose are the result of fitting to Eq. (4).

Figure 8 shows ΓFree and ΓLoose of d67DMPC-37H2O at 285 K plotted against Q2. The Γ’ values also follow the jump diffusion model (Eq. (4)). These results indicate that the translational motions of the loosely bound water and the free water exist below the main transition temperatures.


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Figure 9. Arrhenius plots of the diffusion coefficients (top), the mean residence times (middle), and the mean jump distances (bottom) of d67DMPC-37H2O obtained from Eq. (2), (4) and (6). The filled squares, filled circles, and filled triangles are those of d67DMPC-37H2O. Open squares are those of bulk water [17]. The open triangles and the diamonds are diffusion coefficients of DMPC-35D2O in this study and of DMPC-34D2O in ref [10], respectively.


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Figure 9 shows Arrhenius plots of the diffusion coefficient, the mean residence time and the mean jump distance of d67DMPC-37H2O. The mean jump distance, 〈〉 was calculated from Eq. (6). l =

6 Dτ 0

(6)

The free water shows a similar diffusion coefficient and mean residence time to those of bulk water [17]. The activation energy of the diffusion coefficient and the mean residence time of the free water are Ea(DFree) = 10.5 (±1.2) kJ mol-1, Ea(τ0Free) = 19.0 (±2.5) kJ mol-1, respectively, smaller than the respective values for bulk water, Ea(DBulk

water)

= 18.6 (±0.3) kJ mol-1and

Ea(τ0Bulk water) = 28.9 (±1.0) kJ mol-1. The lower activation energies indicate that the hydrogen bonds of the free water might be more distorted than bulk water. These results indicate that the free water is not the true “free water”. The decrease in the activation energy due to the distortion of the hydrogen bond was also reported in the other systems whose pore wall (mesoporous silicate [22], metal organic framework [17]) is harder than that of the lipid bilayer. The distortion of hydrogen bonds could be commonly caused by the confinement in nanometer scale. More experiments are required to investigate this effect further because the structural properties of water molecules should be investigated by coherent scattering. The diffusion coefficient of the loosely bound water was approximately an order of magnitude smaller than that of the free water and showed no significant temperature dependence. The mean residence time and jump distance for the loosely bound water is longer than that for the free water. The long mean residence time (Ea(τ0Loose) = 27.5 (± 3.2) kJ mol-1) and the mean jump distance (Ea(< l >Loose) = 10.6 (± 3.7) kJ mol-1) might be due to the interaction between water and a head group of a DMPC molecule.


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Figure 10. Plots of AFree (square), ALoose (circle) ATight (triangle) obtained by Eq. (1) and (5) as a function of Q2. The solid lines are the results fitted to Eq. (7).

Figure 10 shows the coefficients of the delta and Lorentz functions (A) obtained by the profile fitting. The peaks of ADelta at 285 and 275 K at Q2 = 2.2 Å-2 are caused by the coherent scattering from the space correlation of alkyl chains. Since all the observed motions are considered as


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diffusive motions, the intensity, with the exception of the peak at Q2 = 2.2 Å-2, is fitted by Eq. (7):

 u2  A = A0 exp − Q2   3   

(7)

where A0 and < u2 > are the intensity at Q = 0 and the mean square displacement, respectively. As shown in supporting information (Figure S2), The Free was quite small even at high temperature. The Eq. (3) and (5) should contain rotational modes both from d67DMPC and water molecules. The intensity of the rotational mode increases with increasing Q and may pushed up the obtained intensity, A, in high Q region. Thus, such the small Free values could be obtained. Other values are also underestimated because they are affected by rotational modes. The detailed discussion for might be difficult because of the difficulty in estimating the contribution from the rotational mode numerically. The value of A0 is proportional to the number of hydrogen atoms because the scattering intensity mainly arises from incoherent scattering. The number of water molecules per lipid molecule (N) was calculated as follows:

 N Tight =   

(8)

 R × + A0 Free  1 − f DMPC 0 Loose

(9)

A

A

A +A

0 Tight

0 Tight

 N Loose =     N Free =   

 R − f DMPC  ×  1 − f DMPC + A0 Free 0 Loose 

A +A

0 Loose

0 Tight

 R × + A0 Free  1 − f DMPC 0 Loose

A +A

0 Free

A

0 Tight

(10)

where R and fDMPC are the molar ratio of water to DMPC (R = 37) and the fraction of incoherent scattering from the d67DMPC (fDMPC = 8.3%), respectively. In this analysis, ATight is assumed to


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include the contribution from DMPC molecules because DMPC shows cooperative dynamics with the tightly bound water.

Figure 11. Plot of the number of water molecules per lipid molecule as a function of temperature obtained by Eq. (8) – (10). Filled circles, filled squares and filled triangles are the number of molecules of free water (NFree), loosely bound water (NLoose), and tightly bound water (NTight), respectively. Open diamonds are the sum of NLoose and NTight.

The obtained NFree, NLoose, and NTight are shown in Figure 11. The average value of NFree remains constant at 23.4 in the measured temperature range, whereas NTight and NLoose monotonically increases and decreases with decreasing temperature, respectively. This result implies that the interaction between water and DMPC molecules becomes stronger with decreasing temperature. On the other hand, the sum of NTight and NLoose is almost constant, which suggests that the hydration range does not change with temperature. This number is close to the number of water molecules per lipid molecule in the hydration shell of DOPC in the liquid crystalline phase (11.6). [30] The values of NFree and (NLoose+NTight) deviated slightly from the


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average values at 285 and 275 K in the gel phase. Also, no significant effect on the diffusion coefficients, the mean residence times, and the mean jump distances was observed for the phase transitions. The present results are inconsistent with the previous results in literature. The hydration numbers obtained by the other experimental methods changed with the phase transition; the hydration number estimated by X-ray scattering in the gel phase was 12.3 [24] and that in the liquid crystalline phase was 25.7 [29], and the hydration number estimated by NMR in the gel phase was less than 4.3 and that in the liquid crystalline phase was 9.7 [25]. This tendency is explained by the drastic change of the area per lipid with the phase transition. [24, 25] It is not surprising that the number of water molecules per lipid molecule depends on experimental methods. The dynamical behavior of water molecules affected by neighboring charge and/or electric dipole moment. So far, the effect of charged agent to the water network has been investigated intensively, but has not been fully understood yet. In the present experiment, the number of temperature below the phase transition temperature is only a few, and further experiments are needed to furnish a more detailed discussion. Even though structural information is not provided by incoherent scattering data, the present results support a water structure sandwiched between lipid bilayers as follows; the tightly bound water molecules move cooperatively with a DMPC molecule, and the loosely bound water locates very close to the lipid headgroups, i. e., they form the so-called hydration shell, while the free water locates at the central position between bilayers. This schematic image is illustrated in the Table of Contents.


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IV.

Conclusion

The dynamical behavior of the hydration water sandwiched between DMPC bilayers was investigated by QENS with a wide energy transfer range with high energy resolution that covers 3 orders of magnitude time scale, using selective deuterated samples (d67DMPC-37H2O and DMPC-35D2O). The water could be categorized into three types: (1) Free water, whose diffusion coefficient and mean residence time are of the same order of magnitude as those of bulk water, but whose activation energies are smaller than those of bulk water. The free water is slightly affected by the confinement effect. The number of free water molecules per DMPC molecule was almost constant. (2) Loosely bound water, whose diffusion coefficient and mean residence time are approximately one order of magnitude smaller and longer than those of bulk water. The loosely bound water is affected by the hydration with the DMPC molecule. (3) Tightly bound water, which moves cooperatively with DMPC molecules. The phase transitions of the DMPC molecule hardly affected both numbers and dynamical parameters (diffusion coefficients etc.) of each type of water. The numbers of loosely and tightly bound water molecules per DMPC molecule monotonically decreased and increased with decreasing temperature, respectively. On the other hand, the sum of the numbers of the loosely and tightly bound water molecules remained almost constant. These results indicate that the hydration state changes with temperature and that the hydration range is constant.

ACKNOWLEDGMENT The neutron experiment at the Materials and Life Science Experimental Facility of the J-PARC was performed under a user program (Proposal 2014B0338) and research project organized by JPARC Center and CROSS-Tokai (Proposal No. 2012P0402, 2013P0402, 2014P0402). This work


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was supported by JSPS KAKENHI Grant Numbers JP25790005, JP23244088, and JP15K05256. We appreciate experimental support from Dr. K. Shibata at J-PARC Center, JAEA. We also appreciate fruitful discussions with Dr. M. Hishida at the University of Tsukuba.


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References 1. Marrink, S. J.; Berkowitz, M.; Berendsen H. J. C. Molecular dynamics simulation of a membrane/water interface: the ordering of water and its relation to the hydration force. Langmuir 1993, 9, 3122-3131. 2. Zhao, W.; Moilanen, D. E.; Fenn, E. E.; Fayer, M. D. Water at the Surfaces of Aligned Phospholipid Multibilayer Model Membranes Probed with Ultrafast Vibrational Spectroscopy. J. Am. Chem. Soc. 2008, 130, 13927-13937. 3. Kundu, A; Blasiak, B; Lim, J-H.; Kwak, K., Cho, M. Water Hydrogen-Bonding Network Structure and Dynamics at Phospholipid Multibilayer Surface: Femtosecond Mid-IR Pump–Probe Spectroscopy. J. Phys. Chem. Lett. 2016, 7, 741-745. 4. Hishida, M.; Tanaka, K. Long-Range Hydration Effect of Lipid Membrane Studied by Terahertz Time-Domain Spectroscopy. Phys. Rev. Lett. 2011, 106, 158102. 5. Choi, D-H.; Son, H.; Jung, S.; Park, J.; Park, W-Y.; Kwon, O. S. Park, G-S. Dielectric relaxation change of water upon phase transition of a lipid bilayer probed by terahertz time domain spectroscopy. J. Chem. Phys. 2012, 137, 175101. 6. König, S.; Sackmann, E.; Richter, D.; Zorn, R.; Carlile, C.; Bayerl, T. M. Molecular dynamics of water in oriented DPPC multilayers studied by quasielastic neutron scattering and deuterium‐nuclear magnetic resonance relaxation. J. Chem. Phys. 1994, 100, 33073316.


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7. Sharma, V. K.; Mamontov, E.; Anunciado, D. B.; O’Neill, H.; Urban, V. Nanoscopic Dynamics of Phospholipid in Unilamellar Vesicles: Effect of Gel to Fluid Phase Transition. J. Phys. Chem. B 2015 119, 4460. 8. Toppozini, L.; Roosen-Runge, F.; Bewley, R. I.; Dalgliesh, R. M.; Perring, T.; Seydel, T.; Glyde, H. R.; Sakai, V. G.; Rheinstädter M. C. Anomalous and anisotropic nanoscale diffusion of hydration water molecules in fluid lipid membranes. Soft Matter 2015, 11, 8534. 9. Swenson, J.; Kargl, F.; Berntsen P.; Svanberg C. Solvent and lipid dynamics of hydrated lipid bilayers by incoherent quasielastic neutron scattering. J. Chem. Phys. 2008, 129, 045101. 10. 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, 3232−3233. 11. Trapp, M.; Gutberlet, T.; Juranyi, F.; Unruh, T.; Demé, B.; Tehei, M.; Peters, J. Hydration dependent studies of highly aligned multilayer lipid membranes by neutron scattering. J. Chem. Phys. 2010, 133, 164505. 12. Schirò, G.; Fichou, Y.; Gallat, F-X.; Wood, K.; Gabel, F.; Moulin, M.; Härtlein, M.; Heyden, M.; Colletier, J-P.; Orecchini, A.; Paciaroni, A.; Wuttke, J.; Tobias, D. J.; Weik M. Translational diffusion of hydration water correlates with functional motions in folded and intrinsically disordered proteins. Nature Comm. 2016, 6, 6490.


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21. Smith, G. S.; Sirota, E. B.; Safinya, C. R.; PlanoN. A. Clark, R. J. X-ray structural studies of freely suspended ordered hydrated DMPC multimembrane films. J. Chem. Phys. 1990, 92, 4519-4529 22. Aso, M.; Ito, K.; Sugino, H.; Yoshida, K.; Yamada, T.; Yamamuro, O.; Inagaki, S.; Yamaguchi, T. Thermal behavior, structure, and dynamics of low-temperature water confined in mesoporous organosilica by differential scanning calorimetry, X-ray diffraction, and quasi-elastic neutron scattering. Pure Appl. Chem. 2013, 85, 289-305. 23. Teixeira, J.; Bellissent-Funel, M.-C.; Chen, S. H.; Dianoux, A. Experimental determination of the nature of diffusive motions of water molecules at low temperatures. Phys. Rev. A 1985, 31, 1913-1917. 24. Tristram-Nagle, S.; Liu, Y.; Legleiter, J.; Nagle, J.F. Structure of Gel Phase DMPC Determined by X-Ray Diffraction. Biophys. J. 2002, 83, 3324–3335. 25. Faure, C.; Erick, L.; Dufourc, E, J. Determination of DMPC hydration in the Lα and Lβ’ phases by 2H solid state NMR of D2O. FEBS Letters 1997, 405, 263-266. 26. Takata, S.; Suzuki, J.; Shinohara, T.; Oku, T.; Tominaga, T.; Ohishi, K.; Iwase, H.; Nakatani, T.; Inamura, Y.; Ito, T.; Suzuya, K.; Aizawa, K.; Arai, M.; Otomo, T.; Sugiyama, M. The Design and q Resolution of the Small and Wide Angle Neutron Scattering Instrument (TAIKAN) in J-PARC. JPS Conf. Proc. 2015, 8, 036020-036025. 27. Nagle1, J.F.; Katsaras, J. Absence of a vestigial vapor pressure paradox. Pys. Rev. E 1999, 59, 7018-7024.


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Dynamical behavior of hydration water molecules between

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