Broadband Dielectric Spectroscopy on Lysozyme in the Sub-Gigahertz

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Broadband Dielectric Spectroscopy on Lysozyme in the Sub-Gigahertz to Terahertz Frequency Regions: Effects of Hydration and Thermal Excitation Naoki Yamamoto, Kaoru Ohta, Atsuo Tamura, and Keisuke Tominaga J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b01491 • Publication Date (Web): 09 May 2016 Downloaded from http://pubs.acs.org on May 10, 2016

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The Journal of Physical Chemistry

Broadband Dielectric Spectroscopy on Lysozyme in the sub-Gigahertz to Terahertz Frequency Regions: Effects of Hydration and Thermal Excitation

Naoki Yamamoto,1 Kaoru Ohta,2 Atsuo Tamura,1 and Keisuke Tominaga1,2,*

1

Graduate School of Science and 2 Molecular Photoscience Research Center, Kobe University, Rokkodai-cho 1-1, Nada, Kobe 657-8501, Japan

*Corresponding author

Tel. & Fax: +81-78-803-5684, E-mail address: [email protected]

1

ACS Paragon Plus Environment


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Abstract We have performed dielectric spectral measurements of lysozyme in a solid state to understand the effects of hydration and thermal excitation on the low-frequency dynamics of protein. Dielectric measurements were performed under changing hydration conditions at room temperature in the frequency region of 0.5 GHz to 1.8 THz. We also studied the temperature dependence (83 K to 293 K) of the complex dielectric spectra in the THz frequency region (0.3 THz to 1.8 THz). Spectral analyses were performed using model functions for the complex dielectric constant. To reproduce the spectra, we found that two relaxational modes and two underdamped modes are necessary together with an ionic conductivity term in the model function. At room temperature, the two relaxational modes have relaxation times of ~20 ps and ~100 ps. The faster component has a major spectral intensity and is suggested to be due to coupled water-protein motion. The two underdamped modes are necessary to reproduce the temperature dependence of the spectra in the THz region satisfactorily. The protein dynamical transition is a well-known behavior in the neutron scattering experiment for proteins, where the atomic mean-square displacement shows a sudden change in the temperature dependence at approximately 200 K, when the samples are hydrated. A similar behavior has also been observed in the temperature dependence of the absorption spectra of protein in the THz frequency region. From our broadband dielectric spectroscopic measurements, we conclude that the increase in the spectral intensities in the THz region at approximately 200 K is due to a spectral blue-shift of the fast relaxational mode.

2


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Introduction Broadband dielectric spectroscopy (BDS) is a powerful technique for investigating the dynamics of condensed materials.1 Compared to other spectroscopic techniques, such as NMR or neutron scattering, BDS is characterized by the extremely broad frequency region that can be utilized during investigations, which ranges from 10-6 Hz to 1012 Hz. The interaction between matter and radiation in this frequency range is due to the collective orientational relaxation of molecular dipoles and the electric conduction that arises from the movement of charges such as ions and electrons. For non-ionic species, this spectroscopy monitors the dynamics that modulate the dipole moment of the system. The frequency-dependent dielectric constant, which is observable with this spectroscopy, is expressed in terms of the time-correlation function of the total dipole moment of the system. BDS has been applied to various condensed materials, including liquids and polymers. The following expression has often been used to analyze the complex dielectric constant,

ε * (ν ) =

∆ε

[1 + (i2πντ ) ]

α β

+ ε∞

(1),

which is called the Havriliak-Negami function. Here, ν is the frequency; ε∞ is the high-frequency permittivity; and ∆ε, τ, α, and β represent the dielectric relaxation strength, relaxation time, Cole-Cole and Cole-Davidson parameters, respectively. When

β = 1, the expression becomes the Cole-Cole function. Eq. (1) becomes the Debye relaxation function when α =1 and β =1. To describe the dielectric response of material in a broad frequency region, the frequency-dependent complex dielectric constant is usually expressed as a sum of Havriliak-Negami functions. The molecular origins of the 3



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relaxation processes have be discussed by examining the temperature dependence of the relaxation time in detail; for example, by plotting the relaxation time as a function of the inverse of the temperature, one can argue whether the activation process of the relaxation is an Arrhenius type or non-Arrhenius type, such as the type expressed by the Vogel-Fulcher-Tammann equation. Protein dynamics have also been studied by BDS for several decades. The technique is useful in studying global dynamics, such as relaxational modes of proteins, for example, side-chain relaxation, protein internal conformational relaxation, and the dynamics of hydration water on protein molecules.2-17 One of the major purposes of these studies is to clarify how hydration and thermal excitation affect the global motions of proteins, which is very important in understanding the mechanisms of protein functions. The reason is that proteins must be surrounded by a certain number of water molecules to express their functions. Moreover, it is necessary that the temperature is sufficiently high for proteins to perform their functions. Usually, the expression of protein functionality accompanies large-amplitude, global motions of the protein molecules; therefore, it has often been discussed how these motions are coupled with surrounding water molecules and how they undergo thermal excitation. BDS measurements of proteins have been performed for either aqueous solutions with proteins as a solute or solid-state powders of proteins. Harvey and Hoekstra applied BDS for lysozyme, one of the globular proteins, to obtain complex dielectric spectra of 10 MHz to 25 GHz.4 These investigators found two distinct dispersions, which were assigned to two layers of adsorbed water at approximately 0.3 and 10 GHz. Sokolov and coworkers extensively studied the dielectric response of globular proteins, including lysozyme, by changing the hydration level and 4


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temperature.15, 16 Recently, Nakanishi and Sokolov reported the dielectric response from 10 mHz to 3 GHz for lysozyme over a broad temperature range.17 They observed three major processes; the fastest process has a relaxation time of ~30 ps at 293 K, which is considered to be a coupled water-protein motion. Recently, terahertz time-domain spectroscopy (THz-TDS) has enabled us to obtain a complex dielectric constant in the THz frequency region with high accuracy.18-20 THz-TDS is an important tool in extending the high-frequency limit of BDS. In contrast to BDS in the frequency region below the THz region, not only relaxation processes but also underdamped vibrational motions have often been observed in the THz region. That finding is especially true if the system under investigation has periodic structures such as molecular crystals, where intermolecular vibrations or large-amplitude intramolecular vibrations are involved.21 For that case, the dielectric constant is expressed as

ε * (ν ) =

A

ν −ν 2 + iνγ 2 0

+ ε∞

(2)

where ν0 is the center frequency, A is the amplitude, and γ is the damping constant. Similar to previous BDS studies, many experiments have been performed on proteins either in solution or in powder form by THz-TDS. In the case of powder samples, the main focus of the research is to investigate the effects of hydration and thermal excitation on the dynamics in the THz region.22-26 One of the most interesting observations with regard to the spectral measurements in the THz region on the proteins is that the absorption spectra of the protein powder samples show a drastic change in intensity at a certain temperature, at which the samples are hydrated. If the samples are dehydrated, then the spectral intensity of the absorption coefficient increases almost linearly when the temperature increases. On the other hand, if the samples are hydrated, 5



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then the change in the spectral intensity is the same as that of the dehydrated samples in the low-temperature region, but at a certain temperature, the increment from the temperature change in the spectral intensity becomes larger. This behavior has been observed for lysozyme, bacteriorhodopsin, poly-L-glutamic acid, and other proteins.22-26 On the other hand, similar behavior has been observed in neutron scattering experiments: by elastic neutron scattering measurements, one can estimate the atomic mean-square displacement (MSD) of the protein,27, 28 and the temperature dependence of this MSD behaves similarly to the temperature change in the absorption coefficient in the THz region. The MSD is almost proportional to the temperature for dehydrated samples in the temperature dependence experiments, while the MSD changes its temperature increment drastically at approximately 220 K for only the hydrated samples. This phenomenon has been referred to as the protein “dynamical transition (DT)”. A general interpretation of this observation is that the low-frequency modes of the protein become more anharmonic by hydration and the large-amplitude motion is induced by this anharmonicity.28-30 Because the large-amplitude motions in the proteins could be related to their functions, protein DTs have been extensively studied by molecular dynamics simulations30-33 as well as neutron scattering experiments.29, 32-44 Furthermore, biphasic behavior has been observed in a plot of the atomic mean-square displacements of proteins as a function of the temperature with X-ray crystallography45. Similar phenomena have also been observed in other experiments, such as NMR46, Mossbauer spectroscopy47 and low-frequency Raman scattering48. Although protein DT-like behavior has been observed in the THz absorption spectra of proteins and polypeptides, its interpretation at a molecular level has not been established yet. More specifically, it is important to investigate whether we can use the 6


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same mechanism as is used for the interpretation of the protein DTs that are observed in neutron scattering. Therefore, in this work, we aim to scrutinize the effects of hydration and thermal excitation on the complex dielectric spectra of lysozyme from the sub-GHz to THz region, focusing on the understanding of the molecular mechanism of the protein DT-like behavior of the THz absorption spectra. As mentioned before, there are two possible contributions to the complex dielectric constant in the THz frequency region, the relaxational modes (eq. (1)) and the underdamped modes (eq. (2)). Therefore, the following are the questions that are to be answered in this work; 1. Which mode makes a major contribution to the protein DT-like behavior in the THz absorption spectra of lysozyme, the relaxational mode or underdamped mode? 2. If the major contribution is the relaxational mode, then how does the relaxation time of this mode depend on the temperature? We first report the frequency-dependent complex dielectric constants of lysozyme at different hydration levels from 0.5 GHz to 1.8 THz at room temperature, which are analyzed in terms of a sum of relaxational and underdamped modes. We then show the complex dielectric spectra of lysozyme obtained by THz-TDS from 0.3 to 1.8 THz and from 83 to 293 K at various hydration levels. The spectra are analyzed based on the results obtained by broad-band spectral analysis at room temperature. We also investigate the temperature hysteresis of the complex dielectric spectra in the THz region to obtain further insight for the thermal activation of the dynamics upon hydration.

Materials and Methods Lyophilized powder of hen egg white lysozyme was purchased from Sigma-Aldrich (St. 7



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Louis, MO). The powder was dialyzed against distilled water for 3 hours and was lyophilized. For the spectral measurements by the three different apparatuses, all of the samples were prepared by pressing the lyophilized powder into pellets using an oil press and appropriate templates, with a pressure of 10 MPa. The diameter of the pellet samples are 10 mm, 20 mm, and 5 mm for dielectric spectroscopy of sub-GHz to GHz region, sub-THz-TDS, and THz-TDS, respectively. Because the size of the pellet is different, the densities of the samples differ slightly from one another. We estimated the density by measuring the thickness and weight of the sample, which is accounted for when the spectral analysis is performed. The pellet samples were stored in a vacuum for 12 hours at room temperature to make the samples dehydrated. We call the samples that were prepared in this way the dehydrated samples. The hydration degree is shown by the value of h. The definition of h is the gram amount of water per one 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 monitored. As a result, we found that the value of h at the dehydrated state was 0.11. To increase the amount of hydration water, samples were placed in a closed container, which was under a saturated vapor pressure of water at room temperature, for an appropriate duration. For the THz-TDS spectrometers, we used two different photoconductive antenna-based systems to cover a broad frequency range. For the frequency range at approximately 0.18 ~ 3.6 THz (6 ~ 120 cm-1), dipole antennas were used for both the generation and detection of the THz pulses. Details of the setup have been described elsewhere.19, 49 Briefly, a laser system was based on a mode-locked Ti:sapphire laser that was centered at 800 nm with a pulse duration of approximately 10 fs and a repetition 8


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rate of 78 MHz (Integral Pro200, FEMTOLASERS Produktions GmbH). A temporal waveform of the THz pulse was measured by scanning a computer-controlled delay stage. The whole system was enclosed in a box under a flow of dry air to minimize the effect of water vapor absorption. Hereafter, we call this equipment a dipole antenna-based system. To measure spectra in a frequency range that is lower than 0.4 THz, we used a THz-TDS system with spiral antennas for generating and detecting the THz pulses. We used the other mode-locked Ti:sapphire laser with a center wavelength of 800 nm, a pulse duration of less than 100 fs and an 80-MHz repetition rate (Tsunami, Spectra-Physics, Inc.). Generated THz pulses were collimated and focused into the sample by using two gold-coated off-axis parabolic mirrors (diameter = 50.8 mm, focal length = 152.4 mm). After the sample, the THz pulses were recollimated and focused into the photoconductive antenna with two off-axis parabolic mirrors. Temporal profiles of the THz electric field were measured by using a variably delayed pulse of 800 nm. Beam profiles at the sample position were estimated by a knife-edge method. The diameter of the electric field of the THz pulse was found to be approximately 8 mm, which is defined as the amplitude at 1/e of the peak. A typical waveform of the THz pulse generated from this setup is shown in Figure 1 along with the amplitude spectrum. The amplitude spectrum has a frequency region of approximately 0.03 to 0.45 THz (1 ~ 15 cm-1), with a peak at 2 cm-1. As is shown later, for the spectral measurement of the solid-state sample such as protein powders, the frequency regions that are effective for measurements are from 0.3 THz to 1.8 THz for the dipole-antenna system, and they are from 0.1 THz to 0.3 THz for the spiral-antenna based system. For the temperature-dependent measurements in the THz region, we used a 9



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cryostat, OptostatDN (Oxford Instruments plc, UK), which was operated with liquid nitrogen. The complex dielectric spectra were measured from 83 K to 293 K with a temperature interval of 10 K or larger. 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 time-domain method allows us to monitor the changes in both the amplitude and phase of the THz electromagnetic wave. The absorption coefficient (α(ν); ν represents the frequency) and the refractive index (n(ν)) can be obtained with a Fourier transformation of the THz wave.50, 51 The absorption coefficient is described as follows:26

α (ν ) =

πν(1 − e − βhcν ) I (ν ) 3ε 0 hc 2 n(ν )V

(3)

where I (ν ) =

∫

∞

−∞

dte − i 2 πνt M (0 ) ⋅ M (t ) .

I (ν~ ) is the line shape function defined as the Fourier transform of the time-correlation

function of the total dipole moment. Here, β, h, c, ε0, V, and t represent 1/kBT (kB and T are the Boltzmann constant and temperature, respectively), Planck’s constant, the speed of light in a vacuum, the dielectric constant in a vacuum, the volume of the sample and time, respectively. The complex dielectric constants, ε’(ν) (real part) and ε’’(ν) (imaginary part), can be calculated using κ(ν) (= ln10·c·α(ν)/4πν) and n(ν), as follows:

ε ' (ν) = n 2 (ν) − κ 2 (ν), . ε ' ' ( ν ) = 2 n (ν ) ⋅ κ (ν )

(4)

Here, α(ν) is the absorption coefficient. The frequency-dependent complex dielectric constants were measured in the frequency region from 0.5 to 20 GHz at room 10


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temperature (293 K) by using a vector network analyzer (VNA) E5071C (Agilent Technologies), together with a performance probe in a dielectric kit probe 85070E (Agilent Technologies). The probe was impressed into a pellet sample of the protein. The spectral measurements were conducted by a calibration procedure that was performed with air, a short connection, and proper materials with dielectric constants that were similar to those of the samples. We chose n-heptane and ethanol as references for the dehydrated samples and hydrated samples, respectively, whose complex dielectric constants were already reported.

Results Broadband Spectroscopy at Room Temperature We first analyze the frequency-dependent complex dielectric constant of lysozyme from 0.5 GHz to 1.8 THz at room temperature. In the Supporting Information, we show the results of the spectral measurements that were obtained by the three different techniques (Figure S1). Usually, the absolute spectral intensities of the complex dielectric constant obtained by different techniques do not coincide with one another. For the connection between the THz-TDS and sub-THz-TDS measurements, the discrepancy in the spectral intensities is due to the difference in the sample densities. By normalizing the spectral intensities in terms of the sample density, the frequency-dependent complex dielectric constants are smoothly connected between the sub-THz and THz frequency regions, as shown in Figure 2. For the VNA measurements and sub-THz-TDS measurements, there is a frequency gap of 20 GHz to 100 GHz between the two measurements. Therefore, it is not obvious to conclude that the absolute spectral intensities of the two measurements 11



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do not coincide. However, we found that we cannot obtain satisfactory results for the spectral fitting by using some model functions for the complex dielectric spectra from 0.5 GHz to 1.8 THz if we use the raw data. We therefore concluded that this finding arises because the absolute spectral intensities of the VNA measurements and sub-THz-TDS measurements do not coincide, most likely because the dielectric probe might not contact perfectly with the surface of the pellet sample. We multiplied the intensities of the complex dielectric spectra in the sub-GHz to GHz region by a factor of 1.05 to 1.25, to enable the spectral analysis (see below) to be successfully performed. Figure 2 displays the normalized frequency-dependent complex dielectric constant at 293 K at different hydration levels. For the dehydrated state (h = 0.11), there is almost no spectral intensity for the imaginary part in the sub-GHz to GHz frequency region. When the sample is hydrated, a spectral component is observed in the imaginary part from the sub-GHz to THz region. The spectral intensity in the region from the GHz to THz region increases almost linearly to the hydration level, which indicates that the spectral increase is related to the hydration water.

One-relaxational mode model We performed spectral analyses for the complex dielectric spectra using a model function, which was determined in the following way. Nakanishi and Sokolov reported the temperature dependence of the complex dielectric spectra of hydrated lysozyme up to room temperature from 10 mHz to 3 GHz.17 According to their results, one relaxational mode with a relaxation time of several tens of picoseconds and the electric conductivity contribute to the complex dielectric spectra at room temperature in the frequency region that was investigated. In addition, as discussed later, we found that at 12


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least two underdamped modes are necessary to reproduce the complex dielectric spectra in the THz region from 0.3 to 1.8 THz satisfactorily. Therefore, the following model function is used to analyze the frequency-dependent dielectric constant from the sub-GHz to THz frequency region at room temperature,

ε ∗ (ν ) =

2 Ak σ0 ∆ε + + + ε inf ∑ β 2 2 i 2πνε 0 1 + (i 2πντ ) k =1 ν k −ν + iνγ k

(5)

The first term represents the ionic conductivity, where σ0 and ε0 is the dc-conductivity and vacuum permittivity, respectively. The second term is the relaxation component, where we used a Cole-Cole function. The variables ∆ε, τ, and β are the dielectric strength, the relaxation time, and the stretching parameter of the relaxational mode, respectively. The third term indicates the underdamped modes, which correspond to the vibrational modes in the THz region. Here, Ak, νk, and γk represent the amplitude, center frequency, and damping constant of the kth underdamped mode, respectively. Herein, we call the k = 1 and k = 2 underdamped modes as the low- and high-frequency underdamped modes, respectively. Additionally, εinf is the high-frequency limit of the dielectric constant. The results of the spectral analysis and obtained parameters are shown in Figure S2 and Table S1, respectively, in the Supporting Information. The dielectric strength of the relaxational mode increases as the hydration level increases, which suggests that the relaxational mode is related to the hydration water, as proposed by Khodadadi et al. and Nakanishi and Sokolov.15-17 The relaxation time of 54 ps for h = 0.35 is in agreement with that obtained by Nakanishi and Sokolov at h = 0.36 (~30 ps).17 The value of ε0/σ0 (350 ps) is close to that obtained by the same group, at h = 0.36 (~400 ps). If the stretching parameter β is equal to one, then the relaxation function is 13



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equal to the Debye function. Deviation of the β value from one suggests that the relaxation process is heterogeneous and that there is a distribution for the relaxation times. Here, the value of β is from 0.5 to 0.6, which suggests that the relaxation process is highly heterogeneous.

Two-relaxational mode model Considering the fact that the relaxational mode is highly heterogeneous, as shown by the spectral analysis, we next employ a two-relaxational mode model, where two Cole-Cole functions are included in the model function,

ε ∗ (ν ) =

2 n ∆ε j σ0 Ak +∑ + + ε inf ∑ β 2 2 i 2πνε 0 j =1 1 + (i 2πντ j ) k =1 ν k − ν + iνγ k j

(6)

Here, we define the component with j = 1 and j = 2 as the fast and slow relaxational modes, i.e., τ2 > τ1, respectively. The fitting results are shown in Figure 3, and the obtained parameters are summarized in Table 1. The residual errors are shown for the models in the Supporting Information (Figure S3), which confirms that the two-relaxational mode model gives a better result than the one-relaxational mode model. The relaxation time of the fast relaxational mode is 27 ps for h = 0.35. The amplitude of the fast relaxational mode is almost proportional to the hydration level, which suggests that the relaxational mode is related to the hydration water. The relaxation time of the slow relaxational mode is approximately 100 ps, which is four to five times slower than that of the fast relaxational mode. The amplitude of the slow relaxational mode also tends to increase as the hydration level increases. The values of β1 and β2 are 0.61 and 0.96, respectively, for h = 0.35, which indicates that the fast relaxational mode is more heterogeneous than the slow mode. It should be noted that the fast relaxational mode 14


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has its spectral component in the THz region, while the spectral intensity of the slow relaxational mode is negligible in the frequency region that is higher than 0.3 THz (10 cm-1). The value of ε0/σ0 is 260 ps at h = 0.35. Hereafter, we continue the spectral analyses for the complex dielectric spectra with the two-relaxational mode model.

Temperature and Hydration Dependence of Complex Dielectric Spectra in the THz Region The temperature and hydration dependencies of the complex dielectric spectra of lysozyme in the THz region from 0.3 to 1.8 THz are shown in Figure 4. In Figure 5, we show the temperature dependence of the intensity of the absorption spectra at 0.5 THz and 1.0 THz at different hydration levels. In the dehydrated state, the spectral intensity almost linearly increases as the temperature increases. For the hydrated states, however, the incremental rates of the spectral intensity as a function of temperature becomes greater at approximately 200 K compared with those in the lower temperature region. Furthermore, if the samples are more hydrated, then the change in this increment rate is greater. This observation suggests that the thermal activation and hydration water is related to the change in the increment rate. This behavior is similar to the behaviors observed in the root-mean-square displacement obtained by the neutron scattering experiment that is called the protein DT. It should be noted that in the cases of h = 0.46 and 0.53, the spectral values jump between 263 and 273 K, while no such jump is observed in the lower hydration levels. Later, we will discuss this observation. We here analyze the frequency-dependent complex dielectric constant of dehydrated and hydrated lysozyme in the THz frequency region based on the results that were obtained in the previous section. At 83 K, two underdamped modes are necessary 15



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for reproducing the complex dielectric spectra of the dehydrated sample. It is found that the following model function works well to simulate the complex dielectric spectra of the dehydrated sample for all of the temperatures investigated: 2

Ak + ε inf . 2 k =1 ν − ν − iνγ k

ε ∗ (ν ) = ∑

(7)

2 k

Examples of the analysis are shown for 83 K and 293 K in Figure 6(a). The temperature dependence of the parameters is shown in Figure S4. In the Supporting Information (Figure S5), we compare the result obtained by the one-underdamped mode model with that obtained by the two-underdamped mode model, to show that the latter model is better at describing the spectral signatures. We next perform the spectral analysis for the hydrated states that have h values of 0.34 and 0.53. At room temperature, based on the previous section, the fast relaxational mode is necessary in the model function for the THz frequency region, while the slow relaxational mode does not have its spectral intensity in that frequency region. Therefore, we add the fast relaxational mode to the model function of eq. (7), as follows:

ε ∗ (ν ) =

∆ε 1

1 − (i 2πντ1 )

2

β1

Ak + ε inf . 2 k =1 ν − ν − iνγ k

+∑

2 k

(8)

The room temperature THz spectra are satisfactorily reproduced by eq. (8), and the parameters are listed in Table 1. We analyze the complex dielectric spectra in the THz region by eq. (8) for all of the temperatures. We found that this model function works well to reproduce the experimental results between 203 K and 293 K. Below 203 K, the fast relaxational mode band is red-shifted, and we need only two underdamped modes for the spectral analysis. Consequently, the relaxational mode is no longer necessary. 16


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Examples of the spectral analysis are shown in Figure 6(b) for h = 0.53. Temperature dependences of the parameters for the relaxational modes are shown in Figure 7, and those of the underdamped modes and the constant in the high-frequency limit are shown in Figure S4. Here, we focus on the temperature dependence of the relaxation time of the fast relaxational mode of the hydrated state. The findings show an almost Arrhenius-type temperature dependence. In contrast, the amplitude (∆ε) and the stretch parameter (β) of the relaxational mode do not depend on the temperature at any of the hydration levels (Figure 7).

Temperature Hysteresis in the THz Spectra We next investigate the “temperature hysteresis” that is observed in the complex dielectric spectra only for the hydrated samples. In the measurement, the temperature was first raised from 83 K to 293 K and then decreased to a temperature of 83 K (Figure 8). Here, we show the intensity changes of the imaginary part of the complex dielectric constant at certain frequencies. The complex dielectric spectra at several different temperatures are displayed in the Supporting Information together with the intensity changes of the real part at several frequencies (Figure S6). When h = 0.32, the imaginary part of the complex dielectric spectrum does not show any “hysteresis”; the imaginary part takes the same values when the temperature is increased and decreased. On the other hand, when the hydration level is high (h = 0.59), a temperature hysteresis is observed, as shown in Figure 8; the imaginary part takes on different values in the temperature region between 240 K and 270 K; the values observed with a fall in temperature are greater than those with a rise in temperature in this temperature region. 17



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It should be noted that the increment rate of the imaginary part as a function of temperature greatly changes at approximately 270 K with a rise in temperature, whereas this transition temperature shifts to approximately 250 K with a fall in temperature. We performed spectral analysis for the case of h = 0.59 by the two-mode relaxational mode model (eq. 8). The obtained relaxation time is 300 ps at 250 K and 150 ps at 260 K for the temperature elevation process. On the other hand, when the temperature is decreased, it is 100 ps at 250 K and 70 ps at 260 K (Figure S6). The other parameters of the relaxational mode (β and ∆ε) are almost the same between the processes that involve temperature increases vs. decreases. The temperature dependences of these parameters are summarized in Figure S6. Similarly, the parameters of the two underdamped modes are not affected by the direction of the temperature change.

Discussion Fast relaxational mode The spectral analyses have shown that the fast relaxational mode has an intensity in the complex dielectric constant for the THz frequency region above 200 K. The dielectric strength of this mode is approximately proportional to the amount of the hydration water, which suggests that the fast relaxational mode is strongly related to the dynamics of the hydration water. The relaxation time of the bulk water is 9.6 ps at 293 K,52 and that of the fast relaxational mode is two (h = 0.53) or three times (h = 0.34, 0.41) slower than that of the bulk water (Table 1). Here, we have a question as to whether the fast relaxational mode is due solely to hydration water or to a coupled protein-water motion. We suggest that the fast relaxational mode is not solely due to hydration water but 18


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includes a coupled protein-water motion, for the following qualitative reason: the hydration water molecules are bound to hydrophilic groups on the protein surface, such as –NH2+ and –COO-. Because the obtained relaxation time is two to three times longer than that of bulk water, the interaction between the hydration water and the protein surface is very strong. Therefore, it is natural to suggest that the hydration water molecules “drag” the hydrophilic groups of the protein surface when they are in translational or rotational motion. Some theoretical and experimental studies support this suggestion. Tarek and Tobias performed MD simulation on hydrated powder of lysozyme with an h of 0.3.31 They found that the relaxation time of the rearrangements of the protein-water hydrogen bond network is at approximately 20 ps at room temperature. Their relaxation time is close to that of the fast relaxational mode obtained in this study, which indicates that the fast relaxational mode is related to the reorientation of the hydrogen bond networks of the hydration water. Khodadadi et al. obtained the relaxation time of lysozyme itself using neutron scattering measurements by hydrating the protein with deuterated water.15, 16

Deuteron has a smaller scattering cross-section than a hydrogen atom, and by using

deuterated water, the protein dynamics can be selectively observed by neutron scattering measurements. From the peak frequency of the susceptibility spectra, they estimated the relaxation time of the protein itself. The relaxation time that they obtained is shown in Figure 7, as shown by the blue asterisk symbols. It can be seen that the relaxation time of lysozyme is similar to that of the fast relaxational mode. These theoretical and experimental studies support the suggestion that the fast relaxational mode is due to the coupled dynamics of hydration water and protein. In fact, this conclusion is the same as that obtained by Sokolov and coworkers.15,

17

Theoretical calculations such as MD

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simulations will reveal the molecular aspects of the dynamics and interactions of the surrounding water molecules and protein surfaces. It is interesting to compare our results on the powder sample with those in solution phases. Cametti and coworkers studied concentration dependence of the dielectric properties of lysozyme aqueous solutions in the frequency range from 1 MHz to 50 GHz.13 They observed two different kinds of orientational relaxation of water in the hydration shell; one component, which has a peak at about 100 MHz, is assigned to tightly bound water, and the other component with a peak at 4 – 5 GHz, is attributed to loosely bound water. If we use the one-relaxational mode model, the relaxational band has a peak at around 6 GHz, which is close to the band due to the loosely bound water reported by Cametti and coworkers. Therefore, the hydrated powder samples and the solution phase samples show similar spectral components in the GHz region. Other spectroscopic techniques such as Raman spectroscopy were also applied to study dynamics of water in the hydration shell around proteins.53, 54 Laage and co-workers recently performed MD simulation for lysozyme aqueous solutions. They reported that the reorientation time of the hydration water is dominantly two times slower than for bulk water.55, 56 Bagchi and co-workers calculated the time correlation function of the total dipole moment of the system. They reported that the relaxation time of this correlation function is ~30 ps.57 The range of the hydration level in our experiment is 0.11 < h < 0.54. This range corresponds to the number of water molecules per one lysozyme molecule from 87 to 429. Yang and Rupley reported that the specific heat capacity of lysozyme became constant at h = 0.38, or approximately 300 water molecules per one lysozyme.58, 59 Rupley and Careri also estimated the number of water molecules in the first hydration shell of lysozyme59; 20


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based on the surface area of lysozyme (6.0 x 103 Å2) and a projection area of the water molecule calculated from the planes of the molecules that were orthogonal to the c axis of Ice I (20 Å2); they concluded that 300 water molecules were in the first hydration shell of lysozyme. This calculated value is in good agreement with that obtained with the calorimetric measurement by Yang and Rupley. Based on these estimations for the number of water molecules in the first hydration shell of lysozyme, we conclude that at h = 0.34, the first hydration shell of lysozyme is almost occupied with water molecules. The similarity between the MD simulation results in the solutions, and our experiment on the powder sample suggests that the water molecules in the vicinity of lysozyme are strongly bound to the protein surface and that the dynamics of these water molecules are not influenced by the surrounding water molecules, even in the solution phases. Thus, it is not very surprising that the dynamics of the water molecules in the first solvation shell for the solutions are similar to those in the powder sample, which has low hydration levels. The stretching parameter β indicates the inhomogeneous distribution of the relaxation time. For the fast relaxational mode, this parameter does not show temperature dependence (Figure 7). Recently, Laage and co-workers suggested that the slowdown of the reorientation time of the hydration water compared to the bulk water was mainly (~80%) determined by a topological excluded-volume factor of the protein surface.55, 56; the local shapes of the protein surface, such as the concave and convex characteristics, determine the reorientation time. The heterogeneity of the protein surface could be the origin of the inhomogeneous distribution of the relaxation time. It should be noted that the fast relaxation process with h = 0.53 is faster than that with h = 0.34 in the temperature region from 273 K to 293 K, as shown in Table 1 21



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and Figure 7(a). Furthermore, in the case of h = 0.59, we observe the temperature hysteresis for τ1 in the range from 250 K to 270 K. These observations are interpreted in the following way: there are bulk-like water molecules for h > 0.53 as well as water molecules that are bound strongly to the protein. The bulk-like water molecules are more mobile than the other water molecules for h = 0.34. The mobile water could be those molecules that are in the second hydration layer or those that are loosely bound to the hydrophilic part of the protein surface. The bulk-like mobile water could become a “supercooled” state at low temperatures, similar to bulk water. The hysteresis that is observed at h = 0.59 is presumably due to this supercooled state of the bulk-like water around the protein. From the Arrhenius plot of the relaxation time, τ = τ 0 exp(Ea RT ) , we estimate the activation energy Ea . We here compare the activation energy with that of bulk water. The Arrhenius plots are displayed in Figure S7.60,61 The activation energy Ea obtained from the results with h = 0.34 is 39±6 kJ/mol. The temperature range for fitting the Arrhenius analysis is from 253 K to 293 K, because below 253 K, the error bar of the obtained relaxation time is somewhat larger. We do not estimate the activation energy for h = 0.53 because of the presence of the temperature hysteresis. The activation energy for the fast relaxation is greater than that of bulk water (18 kJ/mol)52. This result might reflect the complexity of the fast relaxation process, which involves the dynamics of the protein itself as well as the dynamics of the hydrogen bonds that are between the hydration water and the protein surface and between the different hydration water molecules.

22


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Slow relaxational mode For the slow relaxational mode, the temperature dependence is not currently available because of the experimental limitation, and only the hydration dependence at room temperature is investigated. We here discuss the possible origins for this relaxational mode. Smith and co-workers proposed that several amino-acid side chains of hydrated lysozyme exhibited some jumping modes in the sub-GHz frequency region in a molecular dynamics simulation combined with neutron scattering experiments at room temperature.62 The time scale of these modes is similar to that of the slow relaxational mode. Oleinikova et al. also observed a relaxational mode with a relaxation time of approximately 500 ps. Based on MD simulation results that indicated the presence of fluctuations of polar sidechains at such time scales, they concluded that the relaxational mode is assigned to be the relaxation of the polar sidechains.10 Therefore, it is possible that the slow relaxational mode is related to motions of the amino-acid side chains that are induced by hydration. Another possible origin of the slow relaxation is related to the heterogeneity of the protein surface. Laage and co-workers suggested that approximately 20% of the total hydration water was more retarded within specific pockets or clefts in the protein surface compared with the main hydration water; this hydration water retained slower reorientation times, which were distributed up to ~10 times slower than bulk water.55 Therefore, it might also be possible that some relaxational modes of the slower hydration water molecules contribute to the slow relaxational mode.

Effect of hydration on vibrational modes

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We found that two underdamped modes are necessary to reproduce the complex dielectric spectra in the THz region. The center frequencies of the two modes are 1.0 ~ 1.6 THz and 2.0 ~ 3.2 THz, and these are dependent on the temperature and hydration levels, which are shown in Figure S4. Existence of the underdamped vibrational modes in the low-frequency region has also been reported in a depolarized light scattering study on aqueous solutions of proteins.53 Depolarized light scattering spectra of aqueous solutions of lysozyme were analyzed by three vibrational bands that were centered at approximately 1.2 THz, 2.4 THz and 3.3 THz.53 The result of this depolarized light scattering study is qualitatively consistent with our results. Because proteins have thousands of vibrational degrees of freedom, there is an almost continuous distribution of the vibrational density of the states (VDOS). In the Debye theory for solid state, the VDOS increases in proportion to the square of the frequency. Therefore, the two vibrational modes are representative, which does not mean that there are only two vibrational modes in the THz region. Above 203 K, the fast relaxational mode overlaps in the THz region; thus, the obtained parameters of the two underdamped modes are rather scattered compared with those below 203 K. Therefore, let us focus on the temperature region below 203 K. It is interesting to note that the center frequency of the low-frequency mode (ν1) shifts the higher side upon hydration below 203 K, while there is almost no difference between the dehydrated and hydrated states in the center frequency of the high-frequency mode (ν2) (Figure S4). It should be noted that Nakagawa and Kataoka reported hydration dependence of the atomic MSD of staphylococcal nuclease obtained by neutron scattering, which could be related to the present observation;63 the slope of the atomic MSD as a function of temperature decreases upon hydration below 150 K.63 These 24


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investigators mentioned that the protein motion is harmonic in this temperature region and the hydration water makes the protein stiff. This finding means that the decrease in the slope upon hydration originates from the increase in the force constants of the low-frequency vibrational motions of the protein. However, the neutron scattering experiments probe the atomic motions of only the protein, whereas the dynamics of both the protein and water contribute to the complex dielectric spectra. Thus, we should be careful when the two experiments are compared. Presumably, theoretical calculations such as MD simulations will help us to understand the relationships between the two types of experiments.

Origin of the protein DT-like behavior in the THz region In the final section, we discuss the origin of the protein DT-like behavior that is observed in the complex dielectric spectra of the protein in the THz region. It is interesting to know which spectral component contributes to the increase in the temperature-dependent dielectric spectra in the THz frequency region when the proteins are hydrated. Figure 9 shows the temperature dependence of the imaginary part of the dielectric constants at 1 THz, reconstructed by the spectral analysis. In the dehydrated state, the spectral intensity that originates from the two underdamped modes increases almost linearly as the temperature increases. Upon hydration, there are two contributions to the spectral intensity at 1 THz, the underdamped modes (green dots in Figure 9) and the relaxational mode (blue dots). As seen from the figure, the spectral intensity due to the underdamped modes changes its slope at approximately 180 K when the temperature is elevated. However, the relaxational mode makes a greater contribution to the protein DT-like behavior. The 25



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spectral component due to the fast relaxational mode increases drastically above 200 K, which causes a sudden change in the complex dielectric spectra when the temperature increases. In other words, below 200 K, the relaxational mode does not have a spectral intensity in the THz frequency region. With a temperature increase, the spectrum of the relaxational mode shifts to the higher frequency side, and above 200 K, the spectrum enters the “frequency window of observation” (THz region). Therefore, we conclude that the protein DT-like behavior observed in the THz region is due to the blue-shift of the relaxational mode, which could originate from a coupled motion of the protein and hydration water. Here, we again emphasize the difference between the neutron scattering experiment and the dielectric measurements; neutron scattering probes the motion of individual atoms, whereas dielectric spectroscopy is sensitive to the total dipole moment, which is a collective observable. In the dielectric spectroscopic measurements, the time-correlation function of the total dipole moment is observed (eq. (3)); thus, the correlation between the different dipole moments µi and µj could become important in the signal. On the other hand, in the neutron scattering experiment, such a correlation is not included in the experimental observables explicitly because they observe the MSD of the individual hydrogen atoms in the protein. Furthermore, in the present dielectric measurements, both the water and protein molecules contribute to the signal, whereas only protein motions are selectively observed in neutron scattering experiments if D2O is chosen as a solvent. Our explanation for the protein DT-like behavior in the complex dielectric spectra is different from the explanation that is often used to interpret the protein DT obtained by neutron scattering. We do not intend to discuss the validity of the 26


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mechanism of the protein DT in neutron scattering in this paper; such a discussion is beyond the scope of this paper, and we must perform MD simulations on protein-water systems to investigate the relationship between the two experiments. Finally, we mention that several groups have already proposed mechanisms that are similar to our conclusions, to explain the protein DTs that are observed by neutron scattering.64-67 Recently, Frauenfelder and coworkers suggested that the protein DT is not a real transition in the protein but that instead, the change in slope of the MSD is caused by the onset of the fluctuations produced by the protein’s hydration shell, in his recent studies performed with coworkers.64-66 Magazù and coworkers concluded that the protein DT is a finite instrumental energy resolution effect, which appears when the characteristic system relaxation time intersects the resolution time.67 These explanations are conceptually the same as that proposed in this work to explain the temperature and hydration dependence of the dielectric spectra of lysozyme.

Conclusions We studied the hydration dependence of the broadband (0.5 GHz to 1.8 THz) dielectric spectra of lysozyme at room temperature. We also studied the temperature (83 K to 293 K) and hydration dependence of the spectra in the THz region (0.3 THz to 1.8 THz). To reproduce the complex dielectric spectra for all of the conditions, we found that two relaxational modes and two underdamped modes are necessary. A major relaxational mode has a relaxation time of a few tens of picoseconds, which is suggested to be due to a protein-water coupled motion. A minor relaxational mode has a relaxation time of approximately 100 ps. The two underdamped modes are required to reproduce the spectra in the THz region satisfactorily. A protein DT-like behavior has often been 27



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observed for the absorption spectra in the THz region for protein samples; at approximately 200 K, the intensity of the absorption spectrum changes its temperature increment in the case of hydrated samples. The origin of this behavior is due to a blue-shift of the fast relaxational spectrum; with an increase in the temperature, the relaxation spectrum shifts to the higher frequency region, and the higher frequency side of the spectrum enters the THz frequency region.

Supporting Information: The parameters obtained by spectral analysis using a one-relaxational mode model, complex dielectric spectra of lysozyme obtained by the three different apparatuses, results of the spectral analyses for the complex dielectric spectra by the one-relaxational mode model, residual obtained by the spectral analysis of the complex dielectric spectra, temperature dependence of the parameters of the two underdamped vibrational modes, results of the spectral analyses for the dehydrated state, results of the measurements and spectral analyses for the temperature hysteresis of the complex dielectric spectra of lysozyme, and the Arrhenius plot of the relaxational time of the fast relaxational mode.

Acknowledgments This work was partially supported by an Industry-Academia Collaborative R&D program from the Japan Science and Technology Agency. The authors thank Professor Masahiro Nakanishi of Fukuoka Institute of Technology, Professor Biman Bagchi of 28


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Indian Institute of Science, and Professor Shinji Saito of Institute of Molecular Science, for their helpful discussions. The authors are grateful to Professor Tetsuo Sasaki and Professor Ohki Kambara of Shizuoka University for their kind help with this work. They also thank Equipment Development Center of Institute for Molecular Science for constructing a mount for the liquid N2 cryostat.

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Proc. Natl. Acad. Sci. USA 2006, 103, 9012-9016. G. Schiro, M. Fomina and A. Cupane, Communication: Protein Dynamical Transition Vs. Liquid-Liquid Phase Transition in Protein Hydration Water. J.

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Chem. Phys. 2013, 139, 121102. G. Schiro, C. Caronna, F. Natali, M. M. Koza and A. Cupane, The "Protein Dynamical Transition" Does Not Require the Protein Polypeptide Chain. J. Phys.

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Dynamical Transition of Protein-Hydration Water. Phys. Rev. Lett. 2010, 104, 098101. B. F. Rasmussen, A. M. Stock, D. Ringe and G. A. Petsko, Crystalline Ribonuclease a Loses Function Below the Dynamical Transition at 220 K. Nature 1992, 357, 423-424. A. L. Lee and A. J. Wand, Microscopic Origins of Entropy, Heat Capacity and the Glass Transition in Proteins. Nature 2001, 411, 501-504. F. Parak, E. N. Frolov, R. L. Mossbauer and V. I. Goldanskii, Dynamics of Metmyoglobin Crystals Investigated by Nuclear Gamma Resonance Absorption.

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Transition in Hydrated Proteins. BBA-Proteins Proteom. 2010, 1804, 15-19. P. Dutta and K. Tominaga, Obtaining Low-Frequency Spectra of Acetone Dissolved in Cyclohexane by Terahertz Time-Domain Spectroscopy. J. Phys.

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Chem. A 2009, 113, 8235-8242. K. Yamamoto, M. H. Kabir, M. Hayashi and K. Tominaga, Low-Frequency Spectra of the Hexamethylbenzene/Tetracyanoethylene Electron Donor-Acceptor Complexes in Solution Studied by Terahertz Time-Domain Spectroscopy. Phys. Chem. Chem. Phys. 2005, 7, 1945-1952. 33



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K. Yamamoto, M. H. Kabir and K. Tominaga, Terahertz Time-Domain

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Spectroscopy of Sulfur-Containing Biomolecules. J. Opt. Soc. Am. B 2005, 22, 2417-2426. R. Buchner, J. Barthel and J. Stauber, The Dielectric Relaxation of Water

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between 0 Degrees C and 35 Degrees C. Chem. Phys. Lett. 1999, 306, 57-63. S. Perticaroli, L. Comez, M. Paolantoni, P. Sassi, L. Lupi, D. Fioretto, A. Paciaroni and A. Morresi, Broadband Depolarized Light Scattering Study of Diluted Protein Aqueous Solutions. J. Phys. Chem. B 2010, 114, 8262-8269. D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis and K. Wynne, Terahertz Underdamped Vibrational Motion Governs Protein-Ligand

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Water Slowdown Next to a Protein. J. Am. Chem. Soc. 2012, 134, 4116-4119. A. C. Fogarty and D. Laage, Water Dynamics in Protein Hydration Shells: The

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Molecular Origins of the Dynamical Perturbation. J. Phys. Chem. B 2014, 118, 7715-7729. R. Ghosh, S. Banerjee, M. Hazra, S. Roy and B. Bagchi, Sensitivity of Polarization Fluctuations to the Nature of Protein-Water Interactions: Study of

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Biological Water in Four Different Protein-Water Systems. J. Chem. Phys. 2014, 141, 22D531. P. H. Yang and J. A. Rupley, Protein--Water Interactions. Heat Capacity of the

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McMahon, I. R. Stroe, J. Swenson and R. D. Young, A Unified Model of Protein 65.

Dynamics. Proc. Natl. Acad. Sci. USA 2009, 106, 5129-5134. H. Frauenfelder, R. D. Young and P. W. Fenimore, Dynamics and the Free-Energy Landscape of Proteins, Explored with the Mossbauer Effect and

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Quasi-Elastic Neutron Scattering. J. Phys. Chem. B 2013, 117, 13301-13307. H. Frauenfelder, P. W. Fenimore and R. D. Young, A Wave-Mechanical Model of Incoherent Quasielastic Scattering in Complex Systems. Proc. Natl. Acad. Sci.

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USA 2014, 111, 12764-12768. S. Magazù, F. Migliardo and A. Benedetto, Puzzle of Protein Dynamical Transition. J. Phys. Chem. B 2011, 115, 7736-7743.

35



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1. Parameters obtained by spectral fitting using the two-relaxational-mode model (eq. (6)) for lysozyme at room temperature.

h ~ 0.35

h ~ 0.41

h ~ 0.52

ε0/σ0 /ps

260±10

180±3

90±2

∆ε1

6.7±0.5

10.1±0.4

13.2±0.9

τ1 /ps

27±3

24±2

17±2

β1

0.61±0.01 0.57±0.01 0.67±0.01

∆ε2

1.5±0.4

2.4±0.3

2.3±0.9

τ2 /ps

93±3

141±7

114±7

β2

0.96±0.04 0.85±0.04 0.94±0.08 2

A1 /THz

1.7±0.0

0.92±0.03

1.0±0.0

ν1 /THz

1.7±0.0

1.4±0.0

1.6±0.1

γ1 /THz

2.5±0.1

1.9±0.2

2.6±0.4

A2 /THz

4.4±0.0

5.1±0.0

5.4±0.0

ν2 /THz

3.1±0.0

2.8±0.1

3.1±0.2

γ2 /THz

1.7±0.3

1.3±0.5

7.3±0.5

εinf

2.9±0.0

2.8±0.1

3.1±0.0

2

36


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure captions Figure 1. (a) Typical temporal profile of the THz pulse generated and detected by using spiral antennas and (b) its corresponding amplitude spectrum. Figure 2. Normalized complex dielectric spectra from the sub-GHz to THz region at 293 K obtained by the vector network analyzer (VNA), the spiral-antenna-based THz-TDS, and the dipole-antenna-based THz-TDS systems, at different hydration levels. The real and imaginary parts are shown by the solid and dotted lines, respectively. The hydration levels of the samples are as follows: h ~ 0.35, VNA 0.35, sub-THz 0.35, THz 0.34; h ~ 0.41, VNA 0.42, sub-THz 0.40, THz 0.41; h ~ 0.52, VNA 0.54, sub-THz 0.50, THz 0.53. Figure 3. Results of the spectral analyses for the complex dielectric spectra at h ~ 0.35, ~ 0.41, and ~ 0.52, by the two-relaxational-mode model (eq. (6)). The upper and lower figures are the real and imaginary parts of the dielectric constant, respectively. Figure 4. Temperature dependence of the complex dielectric spectra with different hydration levels obtained by the THz-TDS system at the frequency region of 0.3 to 1.8 THz. Figure 5. Temperature dependence of the spectral intensity of the imaginary part of the complex dielectric constant at 0.5 THz (left) and 1.0 THz (right), at different hydration levels. Figure 6. Results of the spectral analyses for the complex dielectric spectra in the THz region at 83 K and 293 K with h = 0.11 (a) and 0.53 (b) obtained by using eq. (7) and (8), respectively. Figure 7. Temperature dependence of the parameters for the fast relaxational mode obtained by fitting the complex dielectric spectra in the THz region by using eq. (8). Figure 8. Temperature hysteresis observed in the complex dielectric spectra. The spectral values of the imaginary part at several frequency points are plotted as a function of the temperature at low and high hydration degrees (h = 0.32 and 0.59, respectively).

37



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The data points at 0.3, 0.6, and 0.9 THz are shifted upward to distinguish each data domain. Figure 9. Analysis of the temperature dependence of the imaginary part of the dielectric constant. The green dots and blue dots represent the value of the sum of the two underdamped modes (low-frequency and high-frequency) and the value of the fast relaxational mode, respectively. The total values are drawn by the black lines. The plot at h = 0.11 (total) is superimposed on the plots of the hydrated states by grey dots.

38


Page 38 of 57

0.04

(a)

0.02 0.00 -0.02 -0.04

-40

0

40

80

Time / ps

1 Amplitude / arb. units

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Amplitude / arb. units

Page 39 of 57

(b) 0.1 0.01 0.001

0

5

10

15

20

25

30

-1

Wavenumber / cm

Figure 1. N. Yamamoto, et al.

39



-1

-1

-1

-1

Wavenumber / cm 0.1 1 10



Wavenumber / cm 0.1 1 10 20 h = 0.11 (Dehydrated) , , ,

15

ε',ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 57

h ~ 0.35

h ~ 0.52

h ~ 0.41

Nerwork Analyzer THz-TDS, spiral THz-TDS, dipole

10

5

0

ε' ε'' 1

10

100

1000

1

ν / GHz

10

100

1000

ν / GHz

1

10

100

ν / GHz


40


1000

1

10

100

ν / GHz

1000

Page 41 of 57

-1

0.1

1

-1

-1

Wavenumber /cm

Wavenumber /cm

Wavenumber /cm

10

0.1

1

0.1

10

1

10

20

h ~ 0.35 Fit, total Relaxation, fast Relaxation, slow Underdamped, low Underdamped, high

ε'

15

h ~ 0.52

h ~ 0.41

εinf

10

Experiment

5

0 6

4

Fit, total Relaxation, fast Relaxation, slow Underdamped, 1st Underdamped, 2nd Conductivity

3

Experiment

5

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 1 0 1

10

100

1000

1

10

100

1000

1

10

ν / GHz

ν / GHz

100 ν / GHz


41


1000


-1

-1

-1

-1

-1

Wavenumber / cm Wavenumber / cm Wavenumber / cm Wavenumber / cm Wavenumber / cm 10 20 30 40 50 6010 20 30 40 50 60 10 20 30 40 50 6010 20 30 40 50 60 10 20 30 40 50 60

ε'

5.0

250

h = 0.11 (Dehydrated)

h = 0.34

h = 0.21

h = 0.53

h = 0.46

200

4.5

150 100

4.0

K

3.5

250

1.5

200

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 57

1.0

150 100

0.5

K

0.0 0.4

0.8

1.2

ν / THz

1.6

0.4

0.8

1.2

ν / THz

1.6

0.4

0.8

1.2

ν / THz

1.6

0.4

0.8

1.2

ν / THz


42


1.6

0.4

0.8

1.2

ν / THz

1.6

Page 43 of 57

h = 0.11 (Dehydrated) h = 0.21 h = 0.34 h = 0.46 h = 0.53

1.0 0.8 0.6

1.0

h = 0.11 (Dehydrated) h = 0.21 h = 0.34 h = 0.46 h = 0.53

0.8

ε''

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6 0.4

0.4

0.2

0.2

1 THz

0.5 THz 0.0

100

150

200

250

0.0

100

150

200

250

Temperature /K

Temperature /K

Figure 5 N. Yamamoto, et al.

43



(a)

(b)

Wavenumber / cm 10 7

20

30

40

-1

50

-1

Wavenumber / cm

Wavenumber / cm 6010

20

30

40

83 K Fit, total Underdamped, low Underdamped, high

6

50

60

10 7

5

20

30

40

-1

50

-1

Wavenumber / cm 60 10

6

εinf

5

30

40

50

60

εinf

Experiment

Experiment

20

293 K Fit, total Relaxation, fast Underdamped, low Underdamped, high

83 K Fit, total Underdamped, low Underdamped, high

293 K

εinf

Experiment

4

ε'

ε'

4 3

3

2

2

1

1 0

0 Fit, total Underdamped, low Underdamped, high

2.0 1.5

2.0 1.5

ε''

Experiment

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 57

1.0

1.0

0.5

0.5

0.0 0.4

0.8

1.2

ν / THz

1.6

Fit, total Underdamped, low Underdamped, high

Fit, total Relaxation, fast Underdamped, low Underdamped, high

Experiment

Experiment

0.0

0.4

0.8

1.2

1.6

0.4

ν / THz

0.8

1.2

1.6

ν / THz


44


0.4

0.8

1.2

ν / THz

1.6

Page 45 of 57

6

10

20

h = 0.34 h = 0.53 Nakanishi and Sokolov Khodadadi et al.

15

∆ ε1

5

10

4

τ1 / ps

3

10

2

10

1

10

10 5

10

β1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.6

4.0

4.4

4.8

-1

1000/T /K

0 1.0 0.8 0.6 0.4 0.2 0.0 200

220

240 260 280 Temperature / K


45


300


3.0 h = 0.59

h = 0.32

T increase T decrease

T increase T decrease

2.5

2.0

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.3 THz

0.3 THz

0.6 THz

0.6 THz

0.9 THz

0.9 THz

1.2 THz

1.2 THz

1.5

1.0

0.5

0.0 100

150

200

250

Temperature (K)

100

150

200

250

Temperature (K)


46


Page 46 of 57

Page 47 of 57

1.0 0.8

ε''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


h = 0.11 (Dehydrated) Underdamped, low+high (Total)

h = 0.34

h = 0.53

Total Underdamped, low+high Relaxation, fast

Total Underdamped, low+high Relaxation, fast

Total (h = 0.11)

Total (h = 0.11)

0.6 0.4 0.2 0.0

100 150 200 250 Temperature / K

100 150 200 250 Temperature /K

100 150 200 250 Temperature /K


47



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A Table of Contents graphic Hydration dependence of the dielectric spectra of lysozyme

N. Yamamoto et al.

48


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) Typical temporal profile of THz pulse generated and detected by using spiral antennas and (b) its corresponding amplitude spectrum. 117x166mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Normalized complex dielectric spectra from sub-GHz to THz region at 293 K obtained by vector network analyzer (VNA), the spiral-antenna-based THz-TDS, and the dipole-antenna-based THz-TDS systems with different hydration levels. The real and the imaginary parts are shown by the solid lines and the dotted lines, respectively. The hydration levels of the samples are as follows; h ~ 0.35; VNA 0.35, sub-THz 0.35, THz 0.34 , h ~ 0.41; VNA 0.42, sub-THz 0.40, THz 0.41, h ~ 0.52; VNA 0.54, sub-THz 0.50, THz 0.53. 77x33mm (300 x 300 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Results of the spectral analyses for the complex dielectric spectra at h ~ 0.35, ~ 0.41, and ~ 0.52, respectively, by the two-relaxation mode model (eq. (6)). The upper and lower figures are the real and imaginary part of the dielectric constant, respectively. 144x117mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Temperature dependence of the complex dielectric spectra with different hydration levels obtained by the THz-TDS system at the frequency region from 0.3 to 1.8 THz. 94x50mm (300 x 300 DPI)


Page 52 of 57

Page 53 of 57

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Temperature dependence of the spectral intensity of the imaginary part of the complex dielectric constant at 0.5 THz (left) and 1.0 THz (right) with different hydration levels . 100x57mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Results of the spectral analyses for the complex dielectric spectra in the THz region at 83 K and 293 K with h = 0.11 (a) and 0.53 (b) obtained by using eq. (7) and (8), respectively. 124x88mm (300 x 300 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Temperature dependence of the parameters for the fast relaxation mode obtained by fitting of the complex dielectric spectra in the THz region by using eq. (8). 81x37mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Temperature hysteresis observed in the complex dielectric spectra. Spectral values of the imaginary part at several frequency points are plotted as a function of temperature at low and high hydration degrees (h = 0.32 and 0.59, respectively). Data points at 0.3, 0.6, or 0.9 THz are shifted upward to distinguish each data domain. 61x46mm (300 x 300 DPI)


Page 56 of 57

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Analysis of the temperature dependence of the imaginary part of the dielectric constant. Green dots and blue dots represent the value of the sum of the two underdamped modes (low-frequency and highfrequency) and the value of the fast relaxation mode, respectively. The total values is drawn by the black lines. The plot at h = 0.11 (total) is superimposed on the plots of the hydrated states by grey dots. 88x43mm (300 x 300 DPI)


Broadband Dielectric Spectroscopy on Lysozyme in the Sub-Gigahertz

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