Effect of Temperature and Hydration Level on Purple Membrane

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Effect of Temperature and Hydration Level on Purple Membrane Dynamics Studied Using Broadband Dielectric Spectroscopy from Sub-GHz to THz Regions Naoki Yamamoto, Shota Ito, Masahiro Nakanishi, Eri Chatani, Keiichi Inoue, Hideki Kandori, and Keisuke Tominaga J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10077 • Publication Date (Web): 05 Jan 2018 Downloaded from http://pubs.acs.org on January 7, 2018

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The Journal of Physical Chemistry

Effect of Temperature and Hydration Level on Purple Membrane Dynamics Studied Using Broadband Dielectric Spectroscopy from Sub-GHz to THz Regions

Naoki Yamamoto1, Shota Ito2, Masahiro Nakanishi3, Eri Chatani1, Keiichi Inoue2, Hideki Kandori2, Keisuke Tominaga1,4*

1

Graduate School of Science, Kobe University, 1-1 Rokkodai-cho, Nada, Kobe 657-8501,

Japan 2

Graduate School of Engineering, Nagoya Institute of Technology, Gokisho-cho,

Shouwa-ku, Nagoya, 466-8555 Japan 3

Department of Electrical Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-

higashi, Higashi-ku, Fukuoka, 811-0295, Japan 4

Molecular Photoscience Research Center, Kobe University, 1-1 Rokkodai-cho, Nada,

Kobe 657-8501, Japan

*Corresponding author; [email protected]

1 ACS Paragon Plus Environment

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Abstract To investigate the effects of temperature and hydration on the dynamics of purple membrane (PM), we measured the broadband complex dielectric spectra from 0.5 GHz to 2.3 THz using a vector network analyzer and terahertz time-domain spectroscopy from 233 to 293 K. In the lower temperature region down to 83 K, the complex dielectric spectra in the THz region were also obtained. The complex dielectric spectra were analyzed through curve fitting using several model functions. We found that the hydrated states of one relaxational mode, which was assigned as the coupled motion of water molecules with the PM surface, began to overlap with the THz region at approximately 230 K. On the other hand, the relaxational mode was not observed for the dehydrated state. Based on this result, we conclude that the protein-dynamical-transition-like behavior in the THz region is due to the onset of the overlap of the relaxational mode with the THz region. Temperature hysteresis was observed in the dielectric spectrum at 263 K when the hydration level was high. It is suggested that the hydration water behaves similarly to super-cooled liquid at that temperature. The third hydration layer may be partly formed to observe such a phenomenon. We also found that the relaxation time is slower than that of a globular protein, lysozyme and the microscopic environment in the vicinity of the PM surface is suggested to be more heterogeneous than lysozyme. It is


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proposed that the spectral overlap of the relaxational mode and the low-frequency vibrational mode is necessary for the large conformational change of protein.



Introduction Water molecules that surround proteins play crucial roles in the expression of their functions, which often accompany large structural changes of proteins. Properties of the hydration water are influenced by the interaction with the protein surface. Therefore, the dynamics of the water molecules in the vicinity of the protein show complicated features that depend on the chemical characteristics of the protein surface. Because the temperature must be high enough for proteins to function properly, it is fundamental to elucidate the microscopic mechanisms for how hydration and thermal excitation influence the large structural changes of proteins. There are several experimental techniques to investigate the effects of hydration and thermal excitation on the large structural changes of proteins. These include neutron scattering,1-11 Mössbauer spectroscopy,12 NMR,13 low-frequency Raman scattering,14 and thermodynamic measurements.15-17 Broadband dielectric spectroscopy (BDS) is also a powerful tool for studying the dynamics of materials in condensed phases,2, 3, 18-27 because the dielectric response of a material to the external alternating electric field is influenced by microscopic properties such as local structures, intermolecular interactions, and molecular motions. One of the unique features of this technique is its broad frequency range from 10-6 Hz to 1012 Hz.28 Thus, dynamics that modulate the total dipole moment


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of the system as fast as picoseconds can be investigated using this technique. BDS has also been applied to proteins to study the temperature and hydration dependence of dynamics such as reorientational relaxation of the whole molecule, side-chain relaxation, and rotational relaxations of hydration water.29, 30 Recent development of generation and detection techniques using terahertz (THz) radiation has extended the high-frequency limit of BDS. We recently reported dielectric spectra from the sub-GHz to THz region of lysozyme by changing the hydration level at room temperature. We also showed the temperature dependence of the THz spectra. The complex dielectric spectrum of lysozyme in the frequency region from subGHz to THz was interpreted using the following function: n 2  j Ak 0  2   inf  ( )   2  i 2 0 j 1 1  i 2 j  k 1  k    i k 

j

(1)

The first term represents the ionic conductivity, where σ0 and ε0 are the DC-conductivity and vacuum permittivity, respectively. The second term is the relaxation component, where a Cole-Cole function was used. The parameters Δεj, τj, and βj are the dielectric strength, the relaxation time, and the stretching parameter of the j-th relaxational mode, respectively. The third term is the underdamped modes, which correspond to the vibrational modes in the THz region. Here, Ak, k, and γk represent the amplitude, center frequency, and damping constant of the k-th underdamped mode, respectively. εinf is the 5 ACS Paragon Plus Environment


high-frequency limit of the dielectric constant. The following conclusions were made for lysozyme using the spectral analysis with eq. (1); (i) The two-relaxational mode model (n = 2 in eq. (1)) reproduces the experimentally obtained dielectric spectra better than the one-relaxational mode model (n = 1). (ii) The ionic conductivity term and the relaxational modes are not needed to simulate the spectra for the dehydrated protein. (iii) The fast relaxational mode is suggested to be caused by coupled water-protein motion. (iv) Above 200 K, the fast relaxational mode spectrum has its high frequency side in the THz region, where the underdamped modes also have their spectra. (v) At low temperatures below ~200 K, the dielectric spectra of the hydrated and dehydrated states in the THz region are similar. However, the spectral intensities of the hydrated samples become larger than those of the dehydrated state above ~200 K. This observation is similar to a phenomenon called protein dynamical transition (DT), which has often been discussed in the temperature dependence of the atomic mean-square displacement of proteins that is observed by neutron scattering measurement. We found that the DT-like behavior observed in the dielectric spectrum is due to a blue-shift of the spectrum of the relaxational mode with the temperature rise. In this study, we focus on the dielectric response of purple membrane (PM). PM


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is a complex of lipids and a membrane protein, bacteriorhodopsin (BR), which is known to exhibit a proton pump function by the photoexcitation of the chromophore. After photon absorption, several conformational changes occur sequentially in BR, which is referred to as the photocycle.31, 32 Interestingly, if the temperature and the hydration level are not high enough, the photocycle does not occur. The hydration structures of membrane proteins are quite different from those of globular proteins. Membrane proteins are surrounded by lipid bilayers. In the case of PM, the mass ratio of BR and lipids is 3:1. The water molecules are located on the surface of the lipid bilayers as well as on the protein surface. Because the inside of the lipid bilayers is hydrophobic, the hydration water molecules do not go into the inside of the proteinmembrane complex. Therefore, the membrane proteins interact with hydration waters in an indirect manner through the lipid bilayers. On the other hand, globular proteins are surrounded by hydration water molecules in aqueous solutions, thus the interaction between the protein and water is rather direct. Therefore, it is interesting to investigate differences in the dielectric properties in the broad-frequency region between the membrane-protein complex and globular proteins. Several research groups reported temperature and hydration dependence of the dielectric spectra of PM. For example, Buchsteiner et al. performed complex dielectric



measurements from 10-3 to 106 Hz at 150-290 K and neutron scattering experiments to discuss the temperature reversibility of the complex dielectric spectra.33 Ermolina et al. observed an orientation change of PM film upon heating with BDS from 10-2 to 3×109 Hz at 278-343 K.34 Berntsen et al. obtained broadband complex dielectric spectra from 10-2 to 109 Hz at 120-300 K together with calorimetric data to understand the molecular mechanism of the relaxation processes.35 They found that one relaxational mode related to the reorientation of hydration water is blue-shifted as temperature increases. The relaxation time increases up to sub-nanoseconds when the temperature is elevated to 210 K. However, the highest frequency of the measurement region of these previous studies was 3 GHz. At room temperature, the spectral component due to the ionic conductivity dominates the dielectric spectrum below the several GHz region, and it is necessary to lower the temperature to observe dielectric response due to protein motions. We need to extend the frequency region higher than GHz to investigate the protein dynamics in the vicinity of room temperature. Previously, we studied the temperature and hydration dependence of the THz absorption spectrum of PM using THz-TDS.36 In the measurements for temperature dependence, we observed a DT-like behavior in the absorption spectra. Namely, significant differences of the spectral features were observed between the hydrated and


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dehydrated states. At low-temperatures below ~220 K, the absorption spectra of the hydrated and dehydrated states in the THz region behave similarly. However, the spectral intensities of the hydrated samples become larger than those of the dehydrated state above ~220 K. Generally, the protein DT is interpreted such that the low-frequency vibrational modes of proteins become more anharmonic through hydration and large-amplitude motions are induced by the anharmonicity.37 The transition temperature for BR is reported to be 230 K. In this paper, we studied the temperature dependence of the broadband dielectric spectra on PM with a variety of hydration levels to investigate the effects of hydration and thermal excitation on the dielectric response of PM, as well as the molecular origin of the DT-like behavior observed in the THz region. We obtained broadband dielectric spectra from 0.5 GHz to 2.3 THz at 233-293 K. Furthermore, the complex dielectric spectra in the THz region were measured down to 83 K. By analyzing the temperature dependence of the dielectric spectra using model functions, we obtained parameters related to the dielectric response such as the relaxation time on the picosecond time scale. We demonstrated that the DT-like behavior of PM is due to the thermal activation of the relaxational mode, as is the case for lysozyme, whereas the parameters of the relaxational mode (such as the relaxation time) are different from those of lysozyme. We also



investigated the temperature hysteresis of the dielectric spectra, which is only observed in a high hydration level to understand how the dynamics of the hydration water depends on the hydration levels.

Materials and Methods PM of Halobacterium salinarum was purified as described in existing literature.38 A solution of PM was spread on a mortar and put under the vacuum for approximately 24 h. A dried film of PM was ground to obtain a fine powder. The powder sample was pressed into pellets by an oil press with a pressure of 10 MPa. The diameter of the pellet samples was 5 mm. The transmission spectra of the samples were measured using a THz timedomain spectrometer. The pellet sample was removed from the holder to use the diskshaped sample for the dielectric measurements from sub-GHz to 20 GHz. The samples were stored in a vacuum for 12 hours at room temperature to dehydrate the samples. We refer to samples that were prepared in this way as dehydrated samples. The hydration level was defined by the value h, which is the gram amount of water per gram of protein. We determined the amount of remaining hydration water in the dehydrated state as follows: A dehydrated sample was incubated in a vacuum for 2 hours at 95°C, and then, the loss of weight was measured. We found that the value of h at the dehydrated state was


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0.05. To increase the amount of hydration water, the pellet samples were placed in a closed container, which was under vapor pressures of saturated potassium chloride solution and water at room temperature for approximately 24 h to achieve h ~ 0.20 or ~ 0.28, respectively. For the THz-TDS spectrometers, we used a photoconductive antenna-based system. For the frequency range at approximately 0.18 to 3.6 THz (6 to 120 cm-1), dipole antennas were used for both the generation and detection of the THz pulses. Details of the setup have been described in previous literature.39 Briefly, a mode-locked Ti:sapphire laser delivers pulses at 800 nm with a duration of approximately 10 fs at 78 MHz. The whole system was enclosed in a box under a flow of dry air to minimize the effect of water vapor absorption. To perform the temperature-dependent measurement in the THz region, we used a liquid nitrogen cryostat, OptostatDN (Oxford Instruments plc, UK). The experiments were performed from 83 to 293 K with a temperature interval of 10 K or larger. The sample and reference holders were located in a cell that was designed to prevent the evaporation of hydration water. To stabilize the sample temperature and reach thermal equilibrium in each measurement at different temperatures, we waited for at least 10 minutes to perform the measurement after changing the temperature. The absorption coefficient (α(ν), where ν represents the frequency) and the refractive index (n(ν)) can be



obtained with a Fourier transformation of the THz wave.40, 41 The complex dielectric constant, ε’(ν) (real part) and ε’’(ν) (imaginary part), are calculated using the extinction coefficient κ(ν) (= ln10ꞏcꞏα(ν)/4πν) and n(ν). The complex dielectric spectra from 0.5 to 20 GHz were obtained using a vector network analyzer, E5071C (Agilent Technologies), equipped with a performance probe in a dielectric kit probe 85070E (Agilent Technologies). The measurements were performed by impressing the probe into a pellet. The measurements were performed in a temperature chamber (SH-262, Espec Co. Ltd.) to control the temperature from 233 to 293 K. The spectral measurements were conducted by a calibration procedure using air, a short connection, and a proper calibration material. It is desirable that the dielectric constant of a calibration material is close to that of the samples, and the material does not show large dielectric dispersion in the measurement frequency range to prevent calibration errors arising from a small temperature mismatch. We chose decane as the calibration material because the complex dielectric constant is already reported and the dielectric constant is almost constant in the frequency range of the measurement.42 The calibration was performed at each temperature point for the measurement. In the temperature dependent measurements, temperature increase or decrease rate was set to be 5 K/min. We waited for 20 minutes at each temperature to thermally equilibrate the


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sample. We confirmed that no further spectral change occurred after the waiting time.

Results Temperature dependence of dielectric spectrum Figure 1 shows the temperature dependence of the complex dielectric spectra in the frequency range from 0.5 GHz to 2.3 THz. The temperature was raised from 233 K to 293 K. In the figure, the complex dielectric spectra obtained by THz-TDS from 0.3 to 2.3 THz are also shown in the temperature range from 83 K to 223 K. For the spectral analyses, it is needed for adjusting the absolute spectral intensities obtained by the VNA and THzTDS measurements. In fact, we found that we could not obtain satisfactory results for the spectral fitting of the complex dielectric spectra from 0.5 GHz to 2.3 THz by using model functions when we used the raw data. Because the measurement methods and the sample conditions were different for VNA and THz-TDS, the raw spectra obtained by the different experimental setups are not necessarily connected smoothly. The spectral mismatch is probably due to the difference in the sample density between the pellets that were used in VNA and THz-TDS. A difference in the density between the surface and the inside of the pellet samples might also be one of the reasons for the mismatch, because VNA probes the surface of a sample whereas a transmission configuration is used for



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THz-TDS. Therefore, we multiplied the intensities of the complex dielectric spectra obtained by VNA by a factor 0.90 to 1.31, so that the spectral analyses performed reasonably well. The factors are shown in Table S1 in the Supporting Information (SI). For the dehydrated state, the imaginary part is almost zero from 233 to 293 K. Moreover, the spectra in the THz region were almost unchanged at all temperatures. On the other hand, for the sample with h = 0.20, the spectral intensity in the GHz region is not zero at 233 K, and the intensity increases as a function of temperature. Similarly, the spectra in the THz region began to increase at approximately 233 K. For h = 0.28, it was clearly observed that the spectra in the GHz region increased as temperature increased from 233 K, and a blue-shift of the spectra was also observed in the high temperature region.

Spectral analysis of the dehydrated state We performed spectral analyses for the complex dielectric spectra using model functions. According to previous studies for lysozyme,39 two vibrational modes are used in the THz region for the dehydrated state:

Ak   inf . 2 k 1     i k 2

  ( )  

(2)

2 k

As shown in Figure 2, the model function reproduces the experimental data fairly well. 14 ACS Paragon Plus Environment

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All of the parameters for the vibrational modes are almost constant for all temperatures. It should be noted that the two vibrational modes are necessary to reproduce the experimental data satisfactorily. Macromolecules such as proteins usually have many normal modes in the low-frequency region because of the large number of the constituent atoms, which are almost continuously distributed as the vibrational density of the states (VDOS).43-45 Therefore, the two vibrational modes should be regarded as the representatives of all of the low-frequency vibrational modes of PM.

Spectral analysis of the hydrated states In the case of the hydrated states, the imaginary part of the dielectric constant has a nonzero intensity in the GHz region. This means there should be an additional component in the model function for the complex dielectric constant. In the case of hydrated lysozyme, two relaxational modes were added to the model function to obtain good agreement between the experimental results and spectral simulation. Here, we first compared the simulation results of the one-relaxational and two-relaxational cases. We found that the one-relaxational mode model simulated the experimental spectra fairly well. We did not observe much improvement in the spectral simulation, even when another relaxational mode was added to the model function. Moreover, the parameters of the relaxational



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modes cannot be determined uniquely in the two-relaxational mode model. Therefore, we will discuss the results of the spectral analysis obtained from the one-relaxational mode model. Dielectric spectra obtained for h ~ 0.20 and h ~ 0.28 are shown in Figures 3 and 4, respectively, together with the simulation results. For h ~ 0.20, we introduced one ColeCole function as a relaxational mode. The model function is as follows:

  ( ) 

 1  i 2 





2



Ak

2 2 k 1 k    i k

  inf .

(3)

As shown in Figure 3, the model function reproduces the experimental results for all of the measurement temperatures. As seen from the figure, the spectrum of the relaxational mode does not have any intensity in the THz region at 233 K. Above this temperature, the spectrum shifts to the higher frequency side, yielding a contribution in the THz region. The obtained fitting parameters of the relaxational mode are shown in Figure 5. The other parameters are shown in Figure S1 in the SI. The relaxation time τ becomes shorter as temperature increases, reaching approximately 100 ps at 293 K. On the other hand, the dielectric strength Δε and the stretching parameter β are almost independent of temperature. The parameters of the vibrational modes do not depend on temperature. We next discuss the spectral analysis for the more hydrated state of h ~ 0.28. We found that eq. (4) is needed to obtain a better spectral simulation for the higher 16 ACS Paragon Plus Environment

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temperature cases (283 K and 293 K).

  ( ) 

2 0 Ak      inf i 20 1  i 2  k 1 2  2  i k k

(4)

The first term on the right-hand side of the equation is the ionic conductivity term. The fitting results are shown in Figure 4. If the ionic conductivity term is absent, the agreement between the experiment and simulation is not satisfactory, especially in the low-frequency side of the GHz region. Below 273 K, the simulated spectra agree well with the experimentally obtained spectra without the ionic conductivity term. Similar to h ~ 0.20, the spectrum of the relaxational mode does not have a significant intensity in the THz region at 233 K, whereas above 233 K, the spectrum shifts to the higher frequency region, having an intensity in the THz region. The obtained fitting parameters of the relaxational mode are shown in Figure 5. The other parameters are summarized in Figure S1 in the SI. The relaxation time τ becomes shorter as temperature rises. It should be noted that the relaxation time is approximately 3 times shorter than that of h ~ 0.20 at 293 K. The relaxation time τ discontinuously changes when the temperature changes from 253 to 263 K. At 233-253 K, the value of τ is similar to that of h ~ 0.20, and it becomes much shorter than that of h ~ 0.20 above 253 K. The value of β also changes discontinuously from 253 to 263 K. From 233 to 253 K, the value is approximately 0.4, which is close to that of h ~ 0.20; it becomes approximately 0.55 above 17 ACS Paragon Plus Environment


263 K. This phenomenon is similar to the discontinuous change of the complex dielectric spectra that is observed in the THz region for lysozyme.39 The results of the spectral analysis of the hydrated states above 233 K demonstrated that the spectral intensity of the relaxational mode in the THz region is very small at 233 K. Therefore, spectral analyses of the hydrated states below 233 K were performed using eq. (2), in which only two vibrational modes in the THz region were introduced. The spectral simulations for 83, 143, and 203 K are shown in Figures 2, 3, and 4, respectively. The spectra are simulated fairly well using the model function. The obtained fitting parameters, which are shown in Figure S1 in the SI, are almost independent of temperature and close to those obtained by the spectral analysis for the broadband dielectric spectra from 233 to 293 K. Thus, we conclude that the contribution of the vibrational modes to the THz region is almost constant at a temperature range of 83 to 293 K.

Temperature hysteresis Figure 6 compares the dielectric spectra of the hydrated state measured by two different methods. In one method, temperature was raised from 233 to 293 K (T-up measurement). The other method decreases the temperature from 293 to 233 K (T-down measurement).


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For h ~ 0.28, a significant difference was observed in the spectra obtained from the T-up and T-down measurements, which we call a “temperature hysteresis” behavior in the broadband complex dielectric spectra. The result of the spectral analysis is also shown in Figure 6A. For h ~ 0.20, the spectra obtained in the T-up and –down measurements are similar for all temperatures. Consequently, the parameters obtained from the spectral analysis using eq. (4) are similar. In contrast, temperature hysteresis is observed for h ~ 0.28; as shown in Figure 6B, the spectra at 263 K do not overlap with each other. The overall spectral component in the GHz region in the T-up measurement is smaller than that of the T-down measurement. The hysteresis is analyzed by performing a spectral analysis on the T-down spectra in the same manner as the T-up spectra that was described above (i.e., eq. (3) for 233-273 K and eq. (4) for 283-293 K). From the obtained parameters as shown in Figure 6B, the relaxation time τ for the T-down measurement is 1.5 times shorter than that for the T-up measurement at 263 K. Furthermore, the dielectric strength Δε of the T-down measurement is about 1.2 times larger than that of the T-up case. Even though the value of β is somehow different for the T-up and –down cases, the difference was the same extent as those observed in the other temperatures. These results indicate that the hysteresis is due to the changes in the dielectric strength and relaxation time.



Discussion Hydration water We first discuss the hydration water on the surface of the PM. The value of h for the dehydrated state is estimated to be 0.05. There are two possible positions at which water molecules are strongly bound, even in the dehydrated state. One is the interior portion of BR, especially around the retinal Schiff base. The water molecules inside the BR cannot be removed, even if the protein is heated in a vacuum. However, the number of these water molecules is ~10 at most, and thus can be ignored when we discuss the number of hydration water molecules. The other position is the hydrophilic part of the head groups of the lipids and the loop regions among the BR transmembrane helices. These hydrated water molecules are strongly bound to PM, and their motions are severely restricted. This is observed in the absence of the relaxational mode in the dielectric spectra of the dehydrated state. Therefore, when we discuss the hydration water molecules that are mobile and able to fluctuate thermally for the case of h > 0.05, it is necessary to subtract the contribution of the strongly bound water from the value of h. Thus, we define the h value for the mobile hydration water as h = h – h (dehydrated). For the cases of h ~ 0.20 and 0.28, the values of h are 0.15 and 0.23, respectively.


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The hydrophilic accessible surface area of PM is roughly estimated to be 3,200 Å2, whereas the hydrophobic accessible surface area is 9,600 Å2 based on the crystal structure reported by Luecke et al. (PDB ID; 1C3W).46 Most of the hydrophilic area exists at the head groups of the lipids and the loops that connect the transmembrane helices. When the hydration level is sufficiently low, most of the hydration water molecules are expected to exist on the hydrophilic surface. Generally, there are at least two types of hydration water molecules around the head groups of the lipids: strongly bound water molecules, which exist even in the dehydrated state, and moderately bound molecules, which are added upon further hydration.47, 48 Similarly, we interpret that the hydrophilic loops of BR are also hydrated by these two types of hydration water. On the other hand, there is no water molecule on the hydrophobic surface in the crystal structure of BR. Therefore, the tightly and moderately bound hydration water molecules on the hydrophilic surface are the dominant components in PM. This is in sharp contrast with the case of water-soluble globular proteins such as lysozyme, in which their surfaces are expected to be uniformly hydrated by water molecules, even if the hydration level is low. This is because, in the case of the lysozyme example, hydrophobic and hydrophilic areas are mixed together, and thus are uniformly distributed. Rupley and Carei reported that an average hydration area per water molecule is



20 Å2 when lysozyme is hydrated.30 If we assume that this value is also applicable to the hydrophilic surface area of PM, the number of water molecules in the first hydration layer on the hydrophilic surface is simply estimated to be approximately 160. Based on this number, the value of h is estimated to be approximately 0.10 when the first hydration layer on the hydrophilic surface is fully occupied. By simply assuming that the same amount of water molecules exist in the second hydration layer, we roughly estimate that the second layer on the hydrophilic surface is fully occupied for h ~ 0.20. Furthermore, we interpret that the third hydration layer is partially formed at h ~ 0.28.

Assignment of the relaxational mode In a previous study,39 we concluded that the relaxational mode in the GHz region on lysozyme at room temperature is due to the protein-water coupled mode, based on comparisons with theoretical studies49-52 and neutron scattering experiments,2, 3 which is consistent with conclusions of other BDS studies.1 We consider that the same conclusion can also be made for the present PM case. The relaxation strength  is 2.3 and 5.6 for h ~ 0.20 and 0.28, respectively, which are roughly correlated with the h value (0.15 and 0.23, respectively). This correlation may lead to the conclusion that the relaxational mode is simply due to the dynamics of the hydration water, and the protein motion has nothing


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to do with it. However, we do not consider this to be the case for the following reason. The relaxation time  is ~100 ps and ~30 ps at 293 K for h ~ 0.20 and 0.28, respectively, which is approximately 10 and 3 times longer than the dielectric relaxation time of water for 9.6 ps at 293 K.53 The hydration water molecules form hydrogen bonds with the hydrophilic groups of PM, such as the hydroxyl group and those of lipids such as – HPO4-.36 Therefore, it is natural to suggest that the hydration water molecules move in association with the hydrophilic groups of the PM surface. Thus, we conclude that the relaxational mode is not only due to the dynamics of the hydration of water molecules, but rather, due to the coupled dynamics of water with PM.

Molecular mechanism of the hydration dependence of the relaxational mode The observation of temperature hysteresis suggests that the hydrated PM behaves similar to super-cooled water around 263 K. Considering that temperature hysteresis was observed at relatively high hydration level conditions (h ~ 0.28) where some of the hydration water molecules exist in the third hydration layer, we suggest that water molecules in the first and second hydration layers behave differently from those in the third layer. The third layer water molecules behave more similarly to those in the bulk water than those in the first and second hydration layers, which are strongly bound to the



surface of PM, hindering their motions. This is also reflected in the fact that the relaxation time for h ~ 0.20 is approximately 3 times longer than that of h ~ 0.28 above 263 K. Note that the stretching parameter for h ~ 0.20 is smaller than that for h ~ 0.28 above 263 K, indicating that the relaxational mode for h ~ 0.20 is more inhomogeneous than that for h ~ 0.28. However, interestingly, the relaxation time as well as the stretching parameter for h ~ 0.28 become the same as those for h ~ 0.20 below 253 K, which is below the temperature hysteresis point (Figure 6). This suggests that once the water molecules in the third hydration layer are “frozen” at low temperatures, these water molecules behave similar to those in the first and second hydration layers. The stretching parameter  is larger at higher temperatures, suggesting that the inhomogeneity of the relaxation time decreases. This is probably due to a bulk-like property of the third hydration layer, which possesses a large dielectric strength  at higher temperatures. The reason is as follows: as shown in Figure 6 and Table S2 in the SI,  is correlated with the residual hydration amount h but is not proportional to it because the increment rate of from h ~ 0.15 to ~ 0.23 is larger than that from h ~ 0.0 to ~0.15. This indicates that at room temperature, the third hydration layer water molecules are more bulk-like, forming hydrogen-bond networks in the third layer. This yields a larger value of  because the correlation between the different dipole moments


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becomes larger. Consequently, the contribution of the third hydration layer dominates the total , and the spectral intensities as well as the values of β resulting from the first and second hydration layers become less important. As a result, the dielectric spectrum appears more “uniform”, and the “effective” inhomogeneity becomes small. In the case of lysozyme, temperature hysteresis was observed for h ~ 0.53 between 253 and 273 K in the dielectric spectra from the sub-GHz to THz region, where the second hydration layer is supposed to be partly formed. Apparently, the hydration amount that is necessary to induce temperature hysteresis is different for PM and lysozyme. This may reflect the fact the interactions on the surface of PM are different than those on the surface of lysozyme. Buchsteiner et al. reported a similar hysteresis phenomenon in the temperature dependence of the real part of the complex dielectric spectra of BR measured at 1 MHz.33 They made dielectric measurements from 10-3 Hz to 106 Hz and chose the highest-frequency side to minimize the influence of conductivity. In the temperature dependence, hysteresis was found for h = 0.35 and 0.45 from 240 to 270 K, and no such trend was observed for h = 0.21. They concluded that the phenomenon was ascribed to freezing and melting of water that existed between the two membrane layers. In this study, we observe hysteresis behavior in the parameters of the relaxational mode such as the relaxation time and dielectric strength in the sub-GHz to THz region,



where there is no influence of the conductivity.

Comparison with globular proteins It is interesting to compare the parameters of the relaxational mode with those of lysozyme, a globular protein, to understand the microscopic details of hydration on the surface of PM. Here, we compare the result of PM for h ~ 0.20 and that of lysozyme for h ~ 0.35. Under these conditions, temperature hysteresis is not observed for both cases, which indicates that all water molecules strongly interact with the surfaces of PM and lysozyme. The relaxation time of PM at h ~ 0.20 is approximately 3 times longer than that of lysozyme (approximately 30 ps at h ~ 0.35).39 This slowdown of the relaxation time suggests that the hydration water molecules on PM are more strongly bound to the surface of PM than lysozyme. The activation energy of the relaxational time obtained by the Arrhenius plot is 66±3 kJ/mol for h ~ 0.20. The value is about twice as large as that of lysozyme (39±6 kJ/mol for h ~ 0.35), supporting the idea that hydration water on PM is more restricted than on lysozyme. Furthermore, the stretching parameter  of PM for h ~ 0.20 is 0.3 to 0.4, which is smaller than that of lysozyme (h ~ 0.35, 0.5 to 0.6).39 This indicates that the inhomogeneity of the distribution of the relaxation time is larger for the PM case than for lysozyme. This is understandable because there are lipid head groups


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and loops on the surface of PM which makes it heterogeneous, whereas the surface of lysozyme is uniform in terms of its chemical constituents.

Role of hydration water for the functional expression Figure 7 shows the spectral intensity of the imaginary part of the complex dielectric constant at 1 THz as a function of temperature. In the figure, the result obtained for the hydrated state is compared with that of the dehydrated state. The spectral intensity of the dehydrated state monotonically changes with temperature. On the other hand, for the case of the hydrated sample, the intensity change is the same as that of the dehydrated state up to 230 K, but above this temperature, the intensity change becomes larger. This behavior resembles that of DT, which has often been observed in the temperature dependence of the atomic root-mean square displacement of the dehydrated and hydrated samples by neutron scattering experiments. In Figure 7, the spectral intensities are decomposed into two contributions: a contribution of the relaxational mode and that of the two vibrational modes. From this figure, it is apparent that the DT-like behavior observed in PM is due to the contribution from the relaxational mode. The spectral component of the relaxational mode is shifted to the THz region from the GHz region as the temperature rises. Kandori et al. showed that the photocycle of BR terminates at the K, L, or M



intermediate states when the temperature is 77, 170, or 230 K, respectively.54-56 Specifically, above 230 K, the M intermediate state experiences a large conformational change which is important for proton transfer. Some theoretical studies suggested that protein low-frequency modes in the THz region are responsible for the protein functional expression.57 A previous study suggested that a photoexcited M intermediate at room temperature possesses the same structure as at 230 K.58 Interestingly, our results show that the spectrum of the relaxational mode starts to have an intensity in the THz region at approximately 230 K, where the vibrational modes also have their spectral intensities. If the vibrational modes are harmonic, nuclei composing the protein simply vibrate around their equilibrium positions and a large conformational change never occurs. Above 230 K, the spectrum of the relaxational mode is overlapped with that of the vibrational mode. Therefore, the relaxational mode and the low-frequency mode may be coupled with one another. Then, a large conformational change may occur. The coupling between the relaxational mode and low-frequency vibrational mode may be important for the conformational change, which is related to the expression of function. In our spectral analysis (eq. (3) or (4)), the relaxational mode and two vibrational modes are independently treated and the coupling between them is not considered. In the future, a functional form considering the coupling may be used.


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Conclusions We investigated the temperature and hydration dependencies of broadband complex dielectric spectra of PM. We found that the relaxational mode, which was ascribed to water-PM surface coupled dynamics, begin to overlap with the THz region at approximately 230 K in the hydrated states, whereas the vibrational modes do not depend on temperature, which was qualitatively similar to the report on a typical globular protein (lysozyme). A temperature hysteresis was observed in the complex dielectric spectra at approximately 263 K for the highly hydrated level. Hydration water molecules on the surface of PM are suggested to be more restricted than those of lysozyme, based on the difference in the relaxation time, the broadness of the relaxational mode, and the activation energy. Because the overlap of the relaxational mode with the THz region began around 230 K, which was close to the temperature where a large conformational change of the M intermediate state occurred, we propose that the thermal coupling of the relaxational modes with low-frequency modes in the THz region was crucial for triggering the large conformational change via anharmonicity of the low-frequency modes.



Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research (KAKENHI) No. 16K17783 from the Japan Society for the Promotion of Science (JSPS). This work was performed by the joint research program of the Molecular Photoscience Research Center at Kobe University.

Supplementary Material Table S1: Parameters used to adjust the complex dielectric spectra obtained by VNA (0.520 GHz) to those obtained by THz-TDS. Table S2: Parameters of the relaxational mode shown in Figure 6 in the main text. Figure S1: The parameters for the vibrational modes, the complex dielectric constant in the high-frequency limit, and the conductivity obtained from curve fitting of the complex dielectric spectra that were measured in the temperature-up measurement Figure S2: The fitting parameters obtained from the curve fitting of the complex dielectric spectra that were measured in the temperature-up and temperature-down measurements using eqs. 2, 3, or 4 for h ~ 0.20 (a) and 0.28 (b).


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Figure Captions Figure 1. The temperature-dependent broadband complex dielectric spectra measured by VNA and THz-TDS at different hydration levels at 233-293 K. The spectra obtained by VNA were multiplied by constants so that the broadband spectra were properly fit using the model functions. The constants are shown in Table S1 in the Supporting Information. See the main text for detail. The complex dielectric spectra obtained by THz-TDS are also shown at 83, 143, and 203 K.

Figure 2. The simulated spectral components at h = 0.05 (dehydrated state) obtained from curve fitting using eq. (2) performed on the complex dielectric spectra that were obtained from the T-up measurements.

Figure 3. The simulated spectral components at h ~ 0.20 obtained from curve fitting using eq. (2) at 83-223 K or eq. (3) at 233-293 K performed on the complex dielectric spectra that were obtained from the T-up measurements.

Figure 4. The simulated spectral components at h ~ 0.28 obtained from curve fitting using eq. (2) at 83-223 K, eq. (3) at 233-273 K, or eq. (4) at 283-293 K performed on the


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complex dielectric spectra that were obtained from the T-up measurements.

Figure 5. The fitting parameters obtained from curve fitting of the complex dielectric spectra, as shown in Figures 3 and 4.

Figure 6. Results of the T-up and T-down measurements. The complex dielectric spectra in the GHz region obtained from the T-up and –down methods and the parameters obtained from curve fittings at h ~ 0.20 (a) and h ~ 0.28 (b), respectively.

Figure 7. Simulated spectral values at 1 THz in the imaginary part of the complex dielectric spectra based on the fitting parameters that are shown in Figure 5 and Table S2.



Figure 1. Yamamoto et al.


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TOC: hydration of purple membrane and a schematic picture of the imaginary part of the complex dielectric spectra of hydrated purple membrane


Effect of Temperature and Hydration Level on Purple Membrane

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