High-sensitivity method for detecting dielectric changes in water driven by biomolecular hydration

Abstract

We previously demonstrated that sub-terahertz irradiation significantly accelerates the formation of hydration structures in protein aqueous solutions under nonequilibrium conditions, immediately after mixing. To monitor this phenomenon, we developed a microwave dielectric measurement technique capable of sensitively detecting time-dependent changes in hydration under sub-terahertz irradiation. This method utilizes the dielectric-dependent modulation of multiply reflected signals in short-path-length samples (Sugiyama et al., Nat. Commun. 14: 2825, 2023). However, the physical origin of the observed signal remained unclear, limiting its broader applicability. In this study, we identify the origin as destructive interference between reflections at the probe–sample interface and the bottom surface of the sample container, which arises uniquely under a short-path-length condition satisfying $d=\lambda /4$. This finding establishes a clear measurement principle and enables direct evaluation of dielectric changes in biomolecular hydration from raw reflection data without converting to complex permittivity.

Significance

Hydration plays a critical role in biomolecular structures and functions, yet its dynamic behavior remains difficult to characterize. Here, we present a simple and sensitive microwave reflection method that exploits destructive interference occurring at a sample path length of $d=\lambda /4$. This approach allows time-dependent detection of hydration-related dielectric changes without requiring conversion to complex permittivity and additional calibration measurements. This technique enables the detection of slow equilibration processes in hydration shells and provides a practical tool for probing hydration phenomena in proteins and other biomacromolecules.

Introduction

In aqueous solutions, water molecules interacting with solute molecules or ions exhibit altered mobility and hydrogen-bonding structure compared to those in pure water; such water is referred to as hydration water. Hydration plays a pivotal role in the expression of biological functions; however, many aspects of its molecular mechanisms remain elusive [1–3]. One major reason is the difficulty in capturing the spatiotemporally heterogeneous dynamics of water that arise from interactions with biomolecular surfaces. For instance, water molecules mutually confined between hydrophobic surfaces exhibit reduced rotational mobility, which leads to suppressed orientational polarization and, consequently, a decrease in the real part of the dielectric permittivity [4–6] as well as an increase in the relaxation time [7].

Broadband dielectric relaxation (DR) spectroscopy in the microwave to millimeter-wave regimes offers a powerful approach to probing water dynamics via orientational polarization processes [8–12]. Liquid water consists primarily of a dynamic network of hydrogen bonds, formed between water molecules with permanent electric dipole moments. Upon application of an electromagnetic (EM) field, these dipoles tend to align along the oscillating EM field and dissipate energy as heat through relaxation processes. DR spectroscopy enables frequency-dependent analysis of the orientational polarization of water dipoles, reflected in the real part of the complex permittivity, and the associated dielectric loss due to energy dissipation, represented by the imaginary part.

Nevertheless, such careful handling of the complex permittivity comprising both real and imaginary parts may hinder its accessibility and limit broader adoption, particularly in interdisciplinary fields such as life sciences. Moreover, capturing subtle, time-dependent changes in the permittivity associated with hydration requires advanced modeling of heterogeneous systems [13–15], as well as specialized knowledge in high-frequency electronics [16,17]. To overcome these limitations, here we have developed a high-sensitivity and experimentally straightforward methodology to assess biomolecular hydration changes based on the reflection characteristics intrinsically linked to the dielectric properties of the sample.

Using an earlier version of this method, we investigated changes in the hydration structure of aqueous lysozyme solutions induced by sub-terahertz (sub-THz, ca. 0.1–0.3 THz) irradiation. We demonstrated that sub-THz irradiation, unlike conventional heating, causes a decrease in the real part of the dielectric permittivity [18]. This result suggests that sub-THz irradiation enhances hydration with a more ordered structure at the hydrophobic surface of lysozyme. Similar irradiation effects have also been observed in structural dynamics of ubiquitin [19] and living cell membranes [20]. In the present study, we clarify the underlying dielectric measurement and establish a broadly applicable methodology for investigating hydration-related phenomena in life sciences.

Materials and methods

Crystalline powder of lysozyme from chicken egg white was purchased from Sigma-Aldrich Co. (Cat. No. 62971) and used without further purification. DNA powder from salmon sperm and cytochrome C powder from horse heart were purchased from Fujifilm-Wako Pure Chemical (Cat. No. 049-31383) and Nacalai Tesque, Inc. (Cat. No. 10429-55), respectively, and used without further purification. Lysozyme and DNA were dissolved in pure water. Cytochrome C was dissolved in a buffer containing 50 mM Tris-HCl (pH=7.6). All solutions were prepared 2 h prior to the measurements, during which hydration was not yet equilibrated.

The reflection coefficient ($S_{11}$) was measured to evaluate the dielectric properties of the aqueous solutions at frequencies ranging from 100 MHz to 14 GHz and at 32 μW (–15 dBm) using a vector network analyzer (VNA) (Rohde & Schwarz, ZVB14). A SUS304 stainless steel coaxial line with Z₀=50 Ω and an outer diameter of 2.2 mm was used as an open-ended coaxial probe (PT292M2024486, KMCO). Further experimental and methodological details are provided elsewhere [18].

Return loss (RL) is expressed in Eq. (1) using the complex reflection coefficient $\mathrm{\Gamma }\left(S_{11}\right)$.

$$\begin{array}{c}\hfill RL(dB)=-20{\log }_{10}|\mathrm{\Gamma }|,|\mathrm{\Gamma }|=\sqrt{{Re\left(S_{11}\right)}^2+{Im\left(S_{11}\right)}^2}\end{array}$$ (1)

The frequency of the RL signal arising from the destructive interference is determined by the relationship among the static dielectric permittivity (${\epsilon }_s$) of the aqueous sample, the wavelength $\lambda$, and the sample path length $d$:

$$\begin{array}{c}\hfill f_{peak}=\frac{c}{\lambda \sqrt{{\epsilon }_s}},\lambda =4d.\end{array}$$ (2)

For $\lambda =4.0mm$ ($\because d=1.0mm$) and the speed of light$c\approx 3.0\times {10}^{8}m{s}^{-1}$, this condition specifies the peak frequency at which the interference occurs. To simulate the frequency dependence of the RL peak ($P_{RL}$), we employed a Lorentzian function as an approximate representation:

$$\begin{array}{c}\hfill P_{RL}(f)=\frac{A}{{1+(\frac{{f-f}_0}{\gamma })}^2},\end{array}$$ (3)

where $f$ is the frequency,$f_0$ is the center frequency of the interference peak, $\gamma$is the linewidth, and $A$is the peak amplitude. The simulation was performed over the frequency range of 1–20 GHz under the following conditions: ${\epsilon }_s$ (reference sample)$=$80, ${\epsilon }_s$ (test sample)$=$78 or 80 (assuming a decrease or constant scenario), $\gamma =$700 MHz, and $A=$0.2 dB. These parameters were chosen arbitrarily to model the interference condition at $d=\lambda /4$ and to visualize the predicted shift in $P_{RL}$, between the reference and test samples.

Results and discussion

Destructive interference-based dielectric sensing in short-path-length samples

In the previous study, we developed a measurement method for monitoring the complex permittivity of aqueous lysozyme solutions under sub-THz irradiation by using a klystron wave source to irradiate 0.1 THz pulsed waves (pulse width: 0.8 μs, average power density: ~20 mW/cm²) from beneath the sample container (Figure 1A). In this method, probing microwaves generated by the VNA were transmitted into the sample through the tip of an open-ended coaxial probe, and the reflected signals were measured via frequency sweeping to evaluate the frequency-dependent dielectric response. To monitor the effects of sub-THz irradiation in situ, the sample thickness must be reduced to a scale comparable to the penetration depth of the sub-THz radiation (~0.1 mm). Consequently, multiple reflections occur due to the short path length (1.0 mm), which typically hinder conventional measurements (Figure 1B). However, this sharp interference peak derived from the multiple reflections does not severely affect the evaluation of the Debye-type relaxation of water, observed over a frequency range of several orders of magnitude. Rather, this signal can be used to sensitively detect changes in sample dielectric permittivity due to sub-THz waves.

Figure 1.

Method of the microwave DR measurement under sub-THz irradiation reported in [18].

(A) Experimental setup and (B) schematic diagram of the multiple reflection signal caused by the short sample pass length ($d$). Both the coaxial probe tip and the polydimethylsiloxane (PDMS) interface behave as open-ended reflections, meaning that no phase inversion occurs upon reflection.

When the sample path length ($d$) is equal to one-quarter of the effective wavelength ($\lambda$/4) of the probing microwaves within the sample (medium), the EM wave reflected from the bottom surface of the sample container travels twice through the sample, corresponding to a total propagation length of $\lambda$/2 (Figure 2A). Under this condition, the reflected wave from the bottom surface acquires a phase shift of $\pi$ relative to the wave reflected at the probe–sample interface. These two reflected components are in antiphase, and their superposition results in destructive interference, causing a pronounced reduction in reflected power. Consequently, a return-loss peak $P_{RL}$ appears at the frequency corresponding to the interference condition $d=\lambda /4$ (Figure 2B).

Figure 2.

Relationship between the return-loss peak ($P_{RL}$) and sample dielectric permittivity.

(A) Principle of the destructive interference occurring in the measurement microwaves generated by VNA. The red arrow indicates the wave reflected (open-end) at the probe-sample interface, and the blue arrow indicates the wave transmitted through the sample and reflected (open-end) at the sample-PDMS interface; the arrow length represents one-quarter wavelength ($\lambda /4$). (B) Schematic of $\lambda$/4 interference condition; relation between the frequency of $P_{RL}$ and the static dielectric permittivity ${\epsilon }_s$ of the sample. The functional plot was generated using Eq. (2) described in Materials and methods. Dashed lines indicate the corresponding frequencies for ${\epsilon }_s=$80 and ${\epsilon }_s=$78.

In practice, the reflected signal includes contributions not only from the interface between the aqueous sample and the container made from polydimethylsiloxane (PDMS), but also from internal reflections within the PDMS layer. Consequently, the resulting interference pattern deviates from the idealized $\lambda$/4 model: the observed $P_{RL}$ appears at a somewhat lower frequency than that predicted based on the nominal sample path length and the dielectric permittivity, and exhibits a spectral width due to the composite nature of the reflected waves. The reflection at the PDMS–air interface can be considered negligible due to the small dielectric permittivity ($\epsilon \approx$2.7 for PDMS vs. 1.0 for air), and is further attenuated after passing through the 2.0-mm-thick PDMS layer (Figure 1A).

Note that the destructive interference arises exclusively from the microwave probe launched by the VNA and reflected within the short-path geometry. Sub-THz irradiation serves as a pump (perturbation) to modulate the sample’s hydration properties and does not participate in the interference path. Therefore, the $\lambda$/4 condition and peak frequencies are determined by the microwave propagation length and boundary conditions at the coaxial open end and the interface of the PDMS container (Figure 2A).

The dielectric response of aqueous biomacromolecular solution in the microwave (MHz–GHz) frequency region comprises the solute-derived relaxation, hydration water-derived relaxations in addition to the main relaxation of bulk water, which is observed near 20 GHz [8,10,20]. Although these components may appear complex, the distribution of multiple relaxations involving Debye processes can generally be expressed by Eq. (4).

$$\begin{array}{c}\hfill {\epsilon }^{*}(\omega )=\sum _i\frac{{\mathrm{\Delta }\epsilon }_i}{1+j\omega {\tau }_i}+{\epsilon }_{\infty }\end{array}$$ (4)

where $\mathrm{\Delta }\epsilon$ is the strength of each relaxation, $\tau$ is the relaxation time, and ${\epsilon }_{\infty }$ is the apparent high-frequency limit in the Debye-type relaxation comprising all vibrational components of the higher frequency regions and the high-frequency limit. Taking the limit of $\omega \to 0$, Eq. (5) gives static dielectric permittivity:

$$\begin{array}{c}\hfill {\epsilon }_s={\mathrm{\Delta }\epsilon }_{sol}+{\mathrm{\Delta }\epsilon }_{hyd}+{\mathrm{\Delta }\epsilon }_{bulk}+{\epsilon }_{\infty },\end{array}$$ (5)

where ${\mathrm{\Delta }\epsilon }_{sol}$, ${\mathrm{\Delta }\epsilon }_{hyd}$ and ${\mathrm{\Delta }\epsilon }_{bulk}$ denote relaxation strengths of solute, hydration water and bulk water, respectively.

According to Eq. (2), if ${\epsilon }_s$ of the aqueous sample decreases from 80 to 78, the frequency of $P_{RL}$ shifts from 8.4 GHz to 8.5 GHz (Figure 2B). Such a decrease in ${\epsilon }_s$ was observed during the rehydration process of powdered lysozyme [18], which occurs because the initially unstable hydration structures formed immediately after mixing gradually evolve into more ordered, hydrophobic hydration shells over time. This behavior can be attributed to a time-dependent decrease in ${\mathrm{\Delta }\epsilon }_{hyd}$, reflecting structural ordering of hydration water around the protein surface rather than a reduction in the amount of hydration water [4–6].

Under the above-mentioned interference condition, $S_{11}$ parameters were measured for both a reference sample and a test sample. While pure water is typically used as the reference, in the present study the objective was to evaluate dielectric changes induced by sub-THz irradiation (or simply by time progress). Therefore, the reference ($S_a$) was defined as the reflection response prior to irradiation, and the test sample ($S_m$) as that after (or during) irradiation of the same protein solution. When the dielectric permittivity remains unchanged upon irradiation, both RL spectra (before and after irradiation) and their difference spectrum ($\mathrm{\Delta }$RL) show no distinctive features (see the example of 50 mM NaCl solution in Figure 3 A–C). In contrast, when the permittivity differs between the states before and after irradiation, the $\lambda$/4 interference condition changes according to Eq. (2) and the frequency at which $P_{RL}$ appears will shift between $S_a$ and $S_m$ (see Figure 3 D–F for 9.1 wt% aqueous lysozyme solution). Thus, even a small difference in dielectric permittivity can cause a measurable shift in $P_{RL}$. Consequently, when the dielectric permittivity differs slightly between the reference and test samples, a distinct peak appears in the$\mathrm{\Delta }$RL spectrum.

Figure 3.

Frequency shift of the interference peak $P_{RL}$ due to changes in dielectric permittivity.

(A, D) Simulated return loss (RL) peak $P_{RL}$ at a sample path length $d$=1.0 mm. (B, E) Simulated difference spectra $\mathrm{\Delta }$RL. (C, F) Experimentally measured $\mathrm{\Delta }$RL spectra for 50 mM NaCl (C) and 9.1 wt% lysozyme solution (F). Each $\mathrm{\Delta }$RL spectrum was obtained by subtracting the pre-irradiation RL ($S_a$) from the post-irradiation RL ($S_m$). Under the interference condition $d$=$\lambda$/4, $P_{RL}$ appears near 8 GHz. Panels A–C show a case where the peak frequency of $P_{RL}$ remains unchanged; D–F show a case where it shifts. For NaCl solution, sub-THz irradiation had no effect on permittivity, and the peak position remains unchanged. For the lysozyme solution, a decrease in permittivity upon irradiation caused a frequency shift of $P_{RL}$ toward higher values [18].

Dielectric characterization using Debye model deviation and calibration

In our previous study, the complex permittivity was determined using a model equation based on open and short calibration data [18], which calibrates the reflection coefficient $S$ and converts it to the complex permittivity ${\epsilon }^{*}$ at each frequency through a Möbius transformation:

$$\begin{array}{c}\hfill {\epsilon }_m^{*}=\frac{{\epsilon }_a^{*}(S_m-S_o)(S_s-S_a)+{\epsilon }_v(S_m-S_a)(S_o-S_s)}{(S_m-S_s)(S_o-S_a)}\end{array}$$ (6)

where, $S_o$, $S_s$, $S_a$, and $S_m$ denote the complex $S_{11}$ parameters for the open, short, standard (reference) sample with known complex permittivity ${\epsilon }_a^{*}$, and test sample with unknown permittivity ${\epsilon }_m^{*}$, respectively. ${\epsilon }_v$ denotes dielectric permittivity of vacuum, which is $1-j0$ (treated as unity). From this set of measured $S_{11}$ parameters, we computed the complex permittivity and defined $\mathrm{\Delta }r$ as the deviation between the measured data and the ideal semicircle predicted from a single Debye-type relaxation in the complex plane (Figure 4A, Nyquist plot) [18]. The peak of this deviation spectrum, denoted $P_{\mathrm{\Delta }r}$, originates from the same physical mechanism as $P_{RL}$ and provides both a qualitative and quantitative indicator of dielectric change near 1 GHz where relaxations of hydration water typically are observed [10,15]. In other words, even subtle changes in the relaxation strength (${\mathrm{\Delta }\epsilon }_{hyd}$) due to sub-THz irradiation can be consolidated into a distinct peak in $P_{\mathrm{\Delta }r}$ (Figure 4A). The intensity of $P_{\mathrm{\Delta }r}$ exhibits a strong correlation with the permittivity change in the test sample around 1 GHz. Our earlier result showed that the $P_{\mathrm{\Delta }r}$ intensity is negatively correlated with the real part of the permittivity and positively correlated with the imaginary part (Figure 4B) [18].

Figure 4.

Quantitative relationship between multiple reflection signal and dielectric properties.

(A) Schematic representation of the multiple reflection signal observed in dielectric relaxation measurements ($d$=1.0 mm), and (B) its relationship with dielectric properties. In (A), a complex permittivity (Nyquist) plot (left) is used to define $\mathrm{\Delta }r$ as the deviation between the measured complex permittivity and the radius $r$ of a semicircle approximating a single Debye-type relaxation. The peak of $\mathrm{\Delta }r$, denoted as $P_{\mathrm{\Delta }r}$, is plotted as a function of frequency (right). In (B), the correlation is schematically shown between the time-dependent changes ($\mathrm{\Delta }t$) in the real part ($\mathrm{\Delta }{\epsilon }^{\prime }$) and imaginary part () of the dielectric permittivity of the lysozyme sample and the variation in the $P_{\mathrm{\Delta }r}$ intensity, as reported in Ref. [18].

Direct evaluation from raw RL spectra without permittivity conversion

In the present study, we demonstrated that changes in the hydration properties, particularly in the relaxation strength ${\mathrm{\Delta }\epsilon }_{hyd}$, between reference and test samples could be evaluated directly from raw RL spectra, without the need to compute complex permittivity. By avoiding such calculation, the measurement principle (i.e., destructive interference occurring under $d$=$\lambda$/4) is made more transparent. Moreover, in this method, evaluating dielectric changes does not require additional port-extension calibration—including offset calibration plane setting and electrical length and loss corrections—after probe installation, whereas the initial system calibration remains necessary. This simplification offers a time-efficient and practical method for detecting dielectric variations.

Specifically, we defined $S_a$ as the RL spectrum of the lysozyme solution before sub-THz irradiation, and $S_m$ as that after irradiation, and calculated ΔRL by subtracting $S_a$ from $S_m$ (Figure 3). Notably, this subtraction cancels out noise signals arising from components other than the sample, such as reflections from the transmission line, resulting in a baseline of $\mathrm{\Delta }$RL ≈ 0 dB (see Supplementary Figure S1 for the raw RL data without subtraction). If strong interference-induced loss occurs at a particular frequency due to changes in the permittivity after irradiation, a characteristic peak in $\mathrm{\Delta }$RL emerges near 8 GHz.

As previously reported [18], when sub-THz irradiation reduces the dielectric permittivity of the sample, the interference conditions for $S_a$ and $S_m$ no longer coincide. Consequently, $P_{RL}$ will shift toward higher frequencies compared to its position in $S_a$ (Figure 3 D–E). This prediction is consistent with experimental RL data, where the observed peak shape in $P_{RL}$ matches the simulated one based on the decrease in permittivity following irradiation (Figure 3F).

It should be noted that the experimental results exhibit broader linewidths and distorted baselines compared to the simulations (compare Figure 3E and F). Specifically for frequencies above 10 GHz, such a difference is attributed to the limitation imposed by the high-frequency range of the VNA used in the measurements. The more general reason is likely attributable not only to differences in relaxation strength (and consequently in ${\epsilon }_s$) between $S_a$and $S_m$, but also to variations in the relaxation time $\tau$ as described in Eq. (4). In this method, the frequency of $P_{RL}$ primarily reflects changes in ${\epsilon }_s$; however, $\tau$, which is affected by temperature and hydration state, also influences the dispersion characteristics. Notably, changes in $\tau$ do not significantly shift the peak position, but they do affect the peak shape, linewidth, and baseline profile, often causing the peak to be obscured by baseline distortion.

As shown in Supplementary Figure S2, similar experiments conducted under the $S_m$ condition with temperature increases ($\mathrm{\Delta }T=1^{\circ }\mathrm{\text{C}}$ or $4^{\circ }\mathrm{\text{C}}$) by irradiation revealed that higher temperatures, which are associated with larger changes in $\tau$ and the resulting dielectric loss, induce baseline distortion in the differential spectrum ($\mathrm{\Delta }RL$). This distortion, likely compounded by peak broadening, causes the interference peak to become buried. At $\mathrm{\Delta }T=4^{\circ }\mathrm{\text{C}}$, the peak was almost completely unobservable.

To investigate the nature of interference-induced changes in $P_{RL}$, we performed additional analysis in which only the sample path length $d$ was varied while maintaining a fixed dielectric permittivity $\epsilon$ for the test sample—either pure water or an aqueous lysozyme solution (Figure 5A). According to the interference condition determined by Eq. (2), the peak frequency of $P_{RL}$ is predicted to shift with sample path length: for $d$=1.0 mm, the predicted frequency is 8.4 GHz; for $d$=1.1 mm, 7.6 GHz; and for $d$=0.9 mm, 9.3 GHz (due to contributions from internal reflections within the sample container, the actual observed peak frequency is slightly lower than the predicted value). Therefore, when $d$ of the test sample $S_m$ is shorter than that of reference sample $S_a$, or when the dielectric permittivity $\epsilon$ of $S_m$ is lower than that of $S_a$ under otherwise identical conditions, the difference $\mathrm{\Delta }RL(S_m-S_a)$ is predicted to exhibit similar characteristics.

Figure 5.

Effect of sample path length ($d$) on $P_{RL}$ profile.

(A) $d$ of the test sample was varied by ±0.1 mm relative to that of the reference sample. (B, C) A shift in the $P_{RL}$ frequency was observed when $d$ was varied, and the observed frequencies were close to those predicted by Eq. (2) for pure water (B) and 2.9 wt% aqueous lysozyme solution (C). Note that this peak shift is not due to changes in dielectric permittivity. Gray curves show the $\mathrm{\Delta }$RL spectra, obtained by subtracting the pre-irradiation spectrum ($S_a$) from the post-irradiation spectrum ($S_m$). The $\mathrm{\Delta }$RL spectra showed a negative correlation when $d$ was increased (1.1 mm) and a positive correlation when $d$ was decreased (0.9 mm). Pearson correlation coefficient $R$ is shown for each comparison. The spectra were obtained by reanalyzing the experimental results performed in Ref. [18]. Smoothed curves were obtained using a locally weighted least-squares error method.

Indeed, when $d$ of $S_m$ was increased from 1.0 mm to 1.1 mm, the resulting $\mathrm{\Delta }RL(S_m-S_a)$ profile exhibited a negative correlation with that after sub-THz irradiation, showing a convex shape below 8 GHz (Figure 5 B and C). Conversely, shortening $d$ to 0.9 mm produced the $\mathrm{\Delta }RL(S_m-S_a)$ profile with positive correlation with that after irradiation, exhibiting a convex shape above 8 GHz (Figure 5 B and C). These results indicate that the shift in $P_{RL}$ observed after sub-THz irradiation can be interpreted as arising from a reduction in the dielectric permittivity of the sample. In both cases, whether due to a decrease in sample path length or permittivity, the $\lambda$/4 interference condition shifts, leading to similar spectral transformations in $P_{RL}$.

The reason why the correlation is not necessarily strong is that RL involves not only a single reflection but also multiple internal reflections within the sample. Consequently, differences in path length $d$ alter the intensity and phase of the interference components, leaving broad residual features in the differential spectrum. In addition, increasing $d$ enhances attenuation due to dielectric loss. When the loss level differs between $S_a$and $S_m$, the absolute RL values also differ, introducing a substantial offset into the differential spectrum (Figure 5B and C).

Hydration-sensitive dielectric response probed by $P_{RL}$

The spectral changes in $P_{RL}$ allow us to gain insight into hydration characteristics of various biomacromolecules. As shown in Figure 6, aqueous solutions of biomacromolecules were prepared approximately two hours before measurement by dissolving powdered samples in water (lysozyme and salmon sperm DNA) or buffer (cytochrome C). Evaluations were performed by taking $S_a$ and $S_m$ as the reflection coefficients measured 18 and 60 minutes, respectively, after sample injection. These were compared against control experiments involving conductive heating, conductive cooling, and room-temperature conditions (Figure 6 A and B). In the cooling and room temperature conditions, no discernible $P_{RL}$ peaks were observed, suggesting that the hydration structure remained unchanged. In contrast, both heating and sub-THz irradiation produced $P_{RL}$, with a marked difference in their effects. Interestingly, although the initial $P_{RL}(S_a)$ intensity before perturbation was nearly identical between the irradiation and heating conditions, the post-perturbation $P_{RL}(S_m)$ intensity was approximately twice as large for irradiation. This enhancement suggests that sub-THz irradiation could promote the formation of a more ordered (i.e. hydrophobic) hydration structure compared to thermal perturbation.

Figure 6.

Evaluation of $P_{RL}$ in biomacromolecular solutions using $S_a$ and $S_m$ as the pre- and post-perturbation RL spectra, respectively.

(A) Perturbations were introduced between 20–30 min after sample injection using 0.1 THz irradiation, conductive heating, or conductive cooling. These resulted in temperature changes of approximately +4 °C, +6 °C, and −4 °C from room temperature (24 °C) within 10 minutes. Experimental details are described in Ref. [18]. (B) Effects of these perturbations on $P_{RL}$ in 9.1 wt% lysozyme solution. (C) Comparison of $P_{RL}$ upon 0.1 THz irradiation among 2.9 wt% lysozyme (Lys), 4.8 wt% cytochrome C (CytC), and 2.0 wt% salmon sperm DNA solutions (DNA). (D) Frequency shift of $P_{RL}$ in $S_a$ and $S_m$ as a function of concentration of the lysozyme (left) or the DNA (right). Smoothed curves were obtained using a locally weighted least-squares error method.

The phenomenon observed in this study appears to be more prominent in biomacromolecules possessing hydrophobic surfaces. We conducted the same evaluation for two other solutes: (i) cytochrome C, an amphiphilic globular protein with a hydrophobic core similar to lysozyme, and (ii) salmon sperm DNA (500–1,000 base pairs), which, despite being amphiphilic, possesses a highly hydrophilic surface due to its sugar–phosphate backbone (Figure 6C). As anticipated, a distinct $P_{RL}$ signal was observed near 8–9 GHz following sub-THz irradiation in cytochrome C solution, with a peak intensity of approximately 0.02 dB. In contrast, the same treatment produced only a weak signal (<0.01 dB) in the DNA solution at a similar frequency. This contrast likely reflects differences in the hydration behavior: cytochrome C has hydrophobic regions that promote ordered hydration structures, whereas the highly hydrophilic surface of DNA reduces such effects.

This contrast supports the hypothesis that interactions between water dipoles and hydrophobic macromolecular surfaces are central to the origin of $P_{RL}$ induced by sub-THz irradiation. This is also consistent with prior reports of reduced dielectric permittivity of water in proximity to hydrophobic surfaces [4,21]. Hydrophobic surfaces may restrict water mobility, leading to lower permittivity and stronger interference effects [18].

Moreover, increasing the concentration of biomacromolecules, which generally possess lower permittivity than bulk water, reduces the overall permittivity of the solution. Thus, the frequency at which $P_{RL}$ occurs should shift toward higher values. Indeed, when the concentrations of lysozyme and salmon sperm DNA were increased, clear blue shifts in the peak position of $P_{RL}$ were observed in both systems (Figure 6D).

It was also observed that in the absence of irradiation, mixing powdered lysozyme with water and allowing the solution to stand at room temperature results in a gradual increase in $P_{RL}$ intensity over a 24-hour period (Figure 7). This indicates that the dielectric properties of the hydration shell slowly evolve toward equilibrium. The sub-THz irradiation appears to accelerate this slow process dramatically, inducing the same dielectric changes within minutes. Thus, the method presented here, which exploits destructive interference at $d=\lambda /4$, enables highly sensitive detection of slow hydration equilibration in biomolecular systems.

Figure 7.

Time-dependent increase in the height of $P_{RL}$ in 2.9 wt% lysozyme solution, without sub-THz irradiation. The reference RL spectrum ($S_a$) was measured 2 hours after mixing, and each test RL spectrum ($S_m$) was measured at the time point indicated in the graph. Smoothed curves were obtained using a locally weighted least-squares error method.

Although not detailed here, our previous work analyzed the distribution of relaxation times and suggested that 0.1 THz radiation selectively perturbs the dynamics of water molecules with short relaxation time—specifically, those involved in relatively weak or no hydrogen bonding within the outer hydration shell of lysozyme [18]. Furthermore, complementary measurements using THz time-domain spectroscopy, which directly probes dielectric response in the sub-THz range, and nuclear magnetic resonance spectroscopy, which reveals structural dynamics on the protein, support the interpretation that the observed decrease in permittivity upon irradiation arises from the formation of a more ordered, hydrophobic hydration structure around the protein [18].

Toward quantitative and general evaluation

Finally, this study demonstrates that the peak height and frequency shift of $P_{RL}$ provide a qualitative indicator of changes in the hydration structure of biological samples, as reflected by variations in $\mathrm{\Delta }{\epsilon }_{hyd}$ (Figures 6 and 7). For quantitative evaluation, $P_{RL}$ can be expressed as $P_{\mathrm{\Delta }r}$, which is defined after permittivity calculation and sharing the same physical origin as $P_{RL}$, to represent its relationship with dielectric properties in a quantitative manner (Figure 4). However, fully quantitative evaluation of hydration-induced permittivity changes remains a subject for future work. The peak intensity of $P_{RL}$, being derived from differential measurements, decreases as the peak frequencies of the two states approach each other (i.e., when the difference in permittivity between the two states is small). Although this relationship allows for quantitative estimation, deriving it experimentally from the peak shape of $P_{RL}$ in high-loss samples such as water remains challenging. This is because dielectric loss also causes peak broadening and baseline distortion/offset, which obscure accurate determination.

Conclusion

We have developed a high-sensitivity and calibration-free dielectric detection method based on destructive interference of reflected microwaves in short-path-length samples. The resulting signal $P_{RL}$, observed under the $d=\lambda /4$ condition, serves as a robust indicator of hydration-related dielectric changes. Sub-THz irradiation was shown to induce a measurable shift and broadening in $P_{RL}$, consistent with the reduced permittivity of the aqueous solution, likely due to enhanced hydrophobic hydration. This method enables time-dependent monitoring of slow hydration equilibration processes and offers a promising platform for broader applications of dielectric spectroscopy in biomolecular science. Future work will focus on improving the quantitative analysis and developing automation for the calibration-free approach. These advancements will enable hydration dynamics to be monitored on timescales comparable to biochemical reactions, providing deeper insight into the influence of temporal variations in hydration structure on biomolecular functions such as enzymatic reactions.

Conflict of interest

The authors declare that they have no conflict of interest.

Author contributions

Masahiko Imashimizu: conceptualization (equal), formal analysis (lead), investigation (lead), methodology (equal), and writing (lead).

Jun-ichi Sugiyama: conceptualization (equal), formal analysis (supporting), investigation (supporting), methodology (equal), and writing (supporting).

Data availability

The data generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Acknowledgements

We thank Masahito Tanaka and Daisuke Satoh for providing access to the klystron wave source. This work was supported by JSPS KAKENHI (project/area numbers JP25K22187 and JP24K01999 to M.I.).