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Abstract
The resonant peaks of biomolecules provide information on the molecules’ physical and chemical properties. Although many biomolecules have resonant peaks in the terahertz region, it is difficult to observe their specific signals in aqueous environments. Hence, this paper proposes a method for determining these peaks. We found the specific resonant peaks of a modified nucleoside, 5-methlycytidine and modified HEK293T DNA in an aqueous solution through baseline correction. We evaluated the consistency of various fitting functions used for determining the peaks with various parameters. We separated two resonance peaks of 5-methlycytidine at 1.59 and 1.97 THz and for artificially methylated HEK293T DNA at 1.64 and 2.0 THz.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Water plays an essential role in biological phenomena and is involved in most biochemical activities [1–4]. Determining the resonant peaks of a biomolecule in water is important because many biomolecules dissolve under aqueous conditions. The structural and chemical properties of biomolecules such as DNA, proteins, and lipids are affected by water [5–7]. Although most biomolecules retain their own properties in an aqueous environment, it is difficult to measure the specific signal about the properties in their solutions. Furthermore, it is difficult to understand the dynamics of biomolecules with complex structures in water because they form intricate patterns with many water molecules.
The terahertz (THz) region covers the spectral signatures associated with the rotational and vibrational motions and inter-molecular interactions of biomolecules [8–12]. Because water molecules are sensitive to THz radiation [13,14], it can be used to determine the water content in biological samples [15–19]. However, they do not detect the specific signals of biomolecules. A recent study revealed that several cancer DNAs showed a resonance signal in aqueous solutions in the THz region [20–24]. This resonance is caused by DNA methylation, which is process of chemical bonding to DNA. Cheon et al. determined a resonant peak of 5-methylcytidine (5-mC) and methylated DNA in an aqueous solution using the frozen spectroscopic technique and baseline correction [20]. They fitted the THz spectrum of the absorption coefficient with two Gaussians; the specific signal of the methylation was located at approximately 1.6 THz, which was obtained by subtracting the baseline representing the absorption of ice [20]. However, the valid bandwidth of the spectrum was only up to 2.0 THz, which did not cover the range of other peaks of 5-mC powder.
In this study, we propose an analytical method to find the resonant peaks of biomolecules in aqueous environments by fitting with Gaussian and Lorentzian functions. We reproduce the curve fitting method of a previous study and identify that there is an additional peak in the extended fitting range [20]. THz time-domain spectroscopy (THz-TDS) is used to obtain the absorption coefficient using the Duvillaret’s algorithm [25–27]. The resonant signals are obtained by using the baseline correction and by fitting the absorption coefficients with Gaussian and Lorentzian functions. We also try to demonstrate a better fitting condition by comparing the consistency and error of the results with various fitting functions and parameters.
2. Experimental setup and sample preparation
2.1 Terahertz time-domain spectroscopy
We used the conventional THz-TDS transmission system to measure the samples. The femtosecond oscillator (Tsunami; Spectra-Physics, CA, USA) was used to produce ultrashort optical pulses with an 800-nm wavelength with a 10-fs pulse duration and an 80-MHz repetition rate. The pulse beam was split into generation and detection parts. The beam path varied by a step size of 10 µm using the movement of the linear motorized stage with a signal integration time of 10 ms at a point. We focused the generation beam on the p-InAs crystal with an incident angle of 78° to produce THz pulses. A pair of parabolic mirrors and a pair of lenses (Tsurupica; Microtech Instrument, Inc., OR, USA) were used to focus the THz pulses to avoid THz signal loss. The THz beam was focused on the center of a sample with a diameter of 1 mm. The THz pulses transmitted through the sample were focused on the detector. A photoconductive antenna (PCA) (TERA8-1; MenloSystems, Germany) was used as a detector.
To reduce the THz absorption of water vapor, the system was sealed inside a container, and its humidity was maintained under 2% by using dry air. Each data point was averaged five times and the time-domain waveform was measured thrice. The reference and sample signals were recorded alternately.
2.2 Samples
5-mC is a modified nucleoside that has a methyl group combined with cytidine. The 5-mC powder exhibits three significant peaks in the THz region, with centers at 1.29, 1.74, and 2.14 THz at 300 K [20]. As it was dissolved in water, these peaks were shrouded because of the relatively large absorption of water molecules even under frozen temperatures (250 K) [20]. The 5-mC powder with purity greater than 99% was purchased from Sigma-Aldrich Corporation. (Missouri, USA). In the solution, 20 mg of the 5-mC was mixed in 100 µl of distilled water.
Artificially methylated DNA of the embryonic kidney cell line (M-293T) sample was produced by the method described in the study of Cheon et al [20]. The DNA was extracted from the cell and methylated via chemical treatment. The sample was dissolved in distilled water at a concentration of 500 ± 7 µg/ml.
2.3 Sample holder
The large absorption of THz signals by water molecules decreases the valid bandwidth of the spectrum and interferes with the detection of dissolved materials. Therefore, we attempted to reduce the terahertz signal loss using the frozen method and a removable cover window. The sample holder contained 75 µl of the sample and froze the sample at 250 K during the measurement. Inside the holder, two thermoelectric cooling devices were attached to the copper plate to uniformly maintain the overall temperature. The thermoelectric cooling devices were also in contact with the water cooler to dissipate heat through the water flow. The z-cut quartz window was located inside the hole of copper plate (Fig. 1(a)).
Fig. 1. Sample holder for maintaining constant temperature of the sample. (a) Structure of sample holder. Inside the holder, a pair of thermoelectric cooling devices were in contact with the copper plate. The thermoelectric devices were cooled by the water cooler. The copper plate had a hole in the middle, and the quartz window was mounted inside the hole. (b) Process of filling liquid sample inside the container. The z-cut quartz window was fixed with a cylinder ring. The 300-µm copper spacer was placed on the z-quartz window. The liquid sample was dropped in the middle of spacer and covered with a Teflon window for 5 min. The Teflon window was removed after the sample was fully frozen, and the experiments were performed at an equilibrium temperature of 250 K.
The sample holder had a single z-cut quartz window to minimize THz absorption by other surrounding materials. In case of two windows, where the liquid sample was placed between the windows, THz signal loss is large because of the four interfaces, even though the z-cut quartz window has a similar refractive index compared with that of ice, which is approximately 2.1 [28]. We reduced the number of interfaces to three by removing a cover window of Teflon as shown in Fig. 1(b). The reference signals were taken with a single quartz window. The thickness of the sample was fixed by the spacer. The spacer was made of copper to transfer heat well, and its thickness was 300 µm. The opening of the spacer is ellipse-shaped with 23 mm long axis and 14 mm short axis; therefore, the sample holding volume is approximately 75 µl with a spacer thickness of 300 µm. To fix the sample inside the holder, we dropped 100 µl of the liquid sample on the quartz window while the holder was placed horizontally (Fig. 1(b)). It was covered with the Teflon window until the whole sample was fully frozen (for 5 min) with a uniform thickness of 300 µm. The holder was rotated carefully by using a rotational motion stage so that the surface of the sample could be perpendicular to the THz beam.
2.4 Optical property calculation
We converted the time-domain data into the frequency-domain ones given by using the fast Fourier transformation. We obtained the optical indices by Fresnel’s equation:
We used the optimization algorithm proposed by Duvillaret et al. [27] to obtain the optical constants. The absorption coefficient spectra of samples were obtained by averaging five different experiments.
2.5 Fitting method
We analyzed the THz absorption spectrum by using the fitting functions made by the “Fitting function builder” and “Nonlinear curve fit” on the OriginPro 9 (OriginLap Corporation, MA, USA), consist of Gaussians (G) and Lorentzians (L) given by Eqs. (3)– (5).
We should obtain reasonable parameters for the baseline curve to separate the signal of the dissolved biomolecules in the solution. We set the boundary condition for the baseline curve with center frequency located over 2 THz. The boundary condition for the other parameters was that their values should be positive.
3. Results and discussions
We obtained the absorption coefficients of the biomolecules dissolved in the aqueous solution at 250 K through THz-TDS and fit the spectra with the functions composed of Gaussians and Lorentzians to separate the specific signals of the biomolecules from the trend of the solution. We found that the resonant signals had two peaks for both 5-mC and M-293T solutions.
3.1 Dependency on fitting bandwidth and number of Gaussian functions
We have performed five independent measurements to obtain the reference and transmission signals through each sample. Each measurement has concurrently taken the reference and sample signals. After taking five sets of data, all the reference signals were averaged yielding the black line with error bars; all the sample signals are indicated by a red line as shown in Fig. 2(a). Figure 2(a) shows the normalized frequency-domain data of the reference and 5-mC aqueous solution in the frozen state (250 K). The valid bandwidth of the reference signal was above 4 THz. However, the bandwidth of 5-mC aqueous solution decreased because THz radiation was attenuated by the large absorption of the water molecules. The valid bandwidth of 5-mC aqueous solution was shown to be up to 3 THz. The error bars after 2.5 THz were ten times larger than those near 1.25 THz. The absorption coefficient was obtained from each data set of reference and sample signals and five independent absorption coefficients were averaged to give Fig. 2(b). This method is more physically accurate as the sample’s coefficient should always be the same, regardless of the condition of the spectrometer. There was a large fluctuation in the absorption spectrum above 2.5 THz. The error bars represent the deviation from the averaged values.
Fig. 2. Frequency-domain signals. (a) Spectra of reference and 5-mC aqueous solution at 250 K. The data were the average of five experiments. (b) Average absorption coefficient of five experiments. Please see the text for details.
We obtained a 0.5 THz extended bandwidth than that of a previous study [20]. The valid spectrum range was 0.2–2.5 THz. We fit the absorption coefficients of the 5-mC aqueous solution with two Gaussians in a fitting range of 0.2–2.0 THz to reproduce the results of the previous study. We also fit the spectrum with the function composed of three Gaussians and four Gaussians in a fitting range of 0.2–2.0 THz to consider the three resonant peaks of the 5-mC powder located at 1.29, 1.74, and 2.14 THz [20].
The low standard error does not ensure that the fitting parameters are reliable and meaningful. A fitting error can be small with functions composed of many arbitrary peaks because the functions compensate for each other, thus minimizing the error. In this case, the values of the fitting parameters are of a random combination; therefore, their consistency and meaning should be checked. We compared the parameters at each fitting function to validate the results.
As the result of two Gaussian fittings, the average center frequency was located at 1.62 THz, which is close to the value obtained by Cheon et al. (Fig. 3(a)) [20]. Fittings with three Gaussians showed unstable results with a large error range. There was no particular trend for the center frequency and peak intensity. For fitting with four Gaussians, the intensity of one of the Gaussians converged to zero or its center frequency diverged to infinity.
Fig. 3. Properties of fitting of absorption coefficients of 5-mC aqueous solution at 250 K with two Gaussians (2G) and three Gaussians (3G) in the range of 0.2–2.0 THz. (a) Center frequencies of the fit Gaussians. #1 and #2 represent the fit Gaussians. (b) Average standard errors of fit combinations.
We compared the standard error, which is given by the following equation:
As the effective range extended, we fitted the spectrum in 0.2–2.5 THz. We found that there was one more peak at approximately 2 THz. We fit the spectrum with three Gaussians (Fig. 4(a)). One Gaussian was used as the background signal (baseline) associated with the ice, and the two Gaussians were fit as the resonant signals of 5-mC dissolved in water. By subtracting the Gaussian baseline, we separated the signal of 5-mC from the solution spectrum. Figure 4(b) shows the peaks composed of two Gaussians with center frequencies located at 1.59 and 1.97 THz.
Fig. 4. Absorption coefficient of 5-mC aqueous solution at 250 K. The fitting range was 0.2–2.5 THz. (a) Fitting the spectrum with three Gaussians. Black circles indicate measured data, and green curve is the fitting line of the measured data. The gray curve is the edge of the Gaussian baseline, and the red circles are the results of subtracting the Gaussian baseline from the measured data. (b) Baseline subtracted absorption coefficient and two fit Gaussians (G #1, G #2) with center frequencies located at 1.59 and 1.97 THz. The two gray bars indicate the frequency of the two peaks of 5-mC powder located at 1.74 and 2.14 THz at 300 K.
By comparing the Gaussian peaks with the peaks of 5-mC powder, both fitting peaks differ by approximately 0.2 THz to the lower frequency from the two major peaks of 5-mC powder located at 1.74 and 2.14 THz [20]. The absorption coefficient of the 5-mC powder at 85 K had peaks at higher frequencies, however, the Gaussian peaks within the solution sample moved to lower frequencies at a lower temperature (250 K). We speculate this was because of the interaction with water molecules.
We also fit the spectrum with four Gaussians in the range of 0.2–2.5 THz to verify the correctness of the fitting method with three Gaussians. As a result, one of the four Gaussians converged to zero. The peak located at approximately 1.29 THz of the 5-mC powder was not noticeable. These results indicate that the fitting range should be sufficiently wide to include target peaks of dissolved biomolecules.
3.2 Dependency on fitting functions
We attempted to fit the resonant peaks with Lorentzian functions to understand the property of the resonant peaks. The physical difference between the Gaussian and Lorentzian functions arises owing to the difference in vibrational population relaxations [29]. The Gaussian curve appears when the incoherent vibrations of molecules are dominant, which is the case of solids. In contrast, the Lorentzian curve is used to fit the peak when the coherent state of molecules is dominant, which is in the case of gases. If the difference between coherent and incoherent vibrations is small, the combined function of the Gaussian and Lorentzian is appropriate.
From the above result, we assume that the origin of our resonant peaks is mostly from the vibration of biomolecules, and not the interaction with the surrounding water molecules. We expected that a Lorentzian fit would provide information on the characteristics of the resonant peaks. We fit the spectrum of the 5-mC aqueous solution with three Lorentzians, and the baseline was fit with the curve of the Lorentzian; the fitting range was 0.2–2.5 THz. Figure 5(a) shows the comparison of the resonant peaks from the baseline of Gaussian or Lorentzian functions. Because the baseline of the frozen solution presented the collective motion of the water molecules, the Lorentzian shape was not adequate. Fitting with three Lorentzians showed large errors in the baselines, which gave random results as shown in Fig. 5(a). The Lorentzian function had a longer tail than that of the Gaussian function with the same full width at half-maximum intensity [30]; thus, a more stable result was obtained from fitting the baseline of the frozen aqueous solution with a Gaussian curve. The resonant peaks from the fittings with the Gaussian baseline presented similar results whether the peaks were fitted with Gaussians or Lorentzians functions. This shows that the fitting results were heavily affected by the subtraction of the baseline curve.
Fig. 5. Absorption coefficient of 5-mC aqueous solution fit in the range of 0.2–2.5 THz. Data were averaged from five experiments. (a) Baseline subtracted absorption coefficients. 3G is the Gaussian baseline subtracted absorption spectrum that is the result of fitting with three Gaussians. 3L is the Lorentzian baseline subtracted spectrum that is the result of fitting with three Lorentzians. 1G + 2L is the Gaussian baseline subtracted spectrum that is the result of fitting with one Gaussian as a baseline and two peaks fitted with Lorentzians. The two gray bars indicate the frequency of the two peaks of 5-mC powder located. (b) Average center frequencies of fitted peaks (excluding baseline peaks). (c) Standard error of each fitting function.
For the fitting of the two Gaussians, the center frequency of the resonant peak was located at 1.8 THz (Fig. 5(b)). It seems to show two peaks as one Gaussian. The center frequencies were almost the same from fitting with three Gaussians and one Gaussian with two Lorentzians. The center frequencies of the two peaks were at 1.59 and 1.97 THz with the Gaussian function and at 1.61 and 1.97 THz with the Lorentzian function. The smallest standard error was achieved for the peaks with the Lorentzians (Fig. 5(c)), which offered a slightly better result than fitting the peaks with Gaussians, although the center frequencies of the peaks were similar.
3.3 Resonant peaks of M-293 T solution
We fit the spectrum of M-293T in the aqueous solution with two functions that had the Gaussian baseline and two peaks with either Gaussians or Lorentzians (Figs. 6(a) and 6(b)). Both results indicate that a new resonant peak was observed at approximately 2 THz, and the previously found peak at approximately 1.64 THz (Fig. 6(c)), which provides almost the same results either with Gaussian or Lorentzian fittings. The two peaks of the M-293 T aqueous solution have a difference of approximately 0.1 THz to the lower frequency with the peaks of 5-mC powder at 300 K from the previous study [20].
Fig. 6. Absorption coefficient of M-293 T aqueous solution at 250 K for the fitting range of 0.2–2.5 THz. (a) Fitting the absorption coefficient spectrum with three Gaussians. G #1 and G #2 represent each Gaussian peak. Baseline (BL) subtracted is the absorption coefficient after subtracting BL from the measured data. (b) Fitting the spectrum with the function composed of one Gaussian and two Lorentzians. Baseline signal was fitted with a Gaussian curve, and the two peaks were fitted with two Lorentzians. L #1 and L #2 represent each Lorentzian peak. (c) Peaks from results of Figs. 6(a) and 6(b). The center frequencies of G #1 and #2 were at 1.64 and 2.0 THz and the center frequencies of L #1 and L #2 are 1.64 and 1.98 THz. The gray bars are the frequencies of the two peaks of 5-mC powder located.
3.4 Fitting quality
The fitting qualities was evaluated with R-square values:
All the R-square values were greater than 0.9990. The average R-square values of the fitting of 5-mC aqueous solution with two Gaussians in the ranges of 0.2–2.0 THz and 0.2–2.5 THz were 0.9993. The average R-square values of fitting the spectrum with three Gaussians with the range of 0.2–2.0 THz was 0.9993, and for 0.2–2.5 THz, 0.9994. The difference in the R-square values was within the margin of standard deviation.
4. Conclusion
In this study, we analyzed the THz absorption spectra of biomolecules in water with the fitting functions and identified resonant peaks by subtracting the baseline. By obtaining the extended THz spectra of 5-mC and M-293T in aqueous solutions with a delicate freezing method (250 K) and the reduction of the interfaces of measurement, we discovered two resonant peaks of the 5-mC and M-293T aqueous solutions in 0.2-2.5 THz range. The best result was obtained from the combination of a Gaussian baseline and Lorentzian functions.
We found that there were a few conditions for the better determination of resonance peaks. The fitting range should be sufficiently wide to contain the locations of target peaks to avoid inconsistency in fitting results or a large fitting error. Further, the appropriate number of fitting functions should be selected with an adequate baseline function.
This technique offers a method for finding resonant signals of biomolecules in an aqueous environment using a fitting procedure with THz absorption spectrum. In the future, we expect that more peaks might be discovered with a wider bandwidth of valid spectrum by utilizing a higher signal-to-noise THz spectroscopy system.
Funding
National Research Foundation of Korea (NRF-2017R1A2B2007827); Institute for Information and Communications Technology Promotion (2017-0-00422); University of Seoul.
Acknowledgments
The work was partly supported by the Institute for Information & communications Technology Promotion (IITP) grant funded by the Korean government (MSIT) (No. 2017-0-00422, Cancer DNA demethylation using ultra-high-power terahertz radiation), by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (NRF-2017R1A2B2007827), and supported by the 2019 sabbatical year research grant of the University of Seoul. We thank Moran Choi for assistance with the producing the DNA solution sample. All figures were drawn by Seo-Yeon Jeong, one of the authors.
Disclosures
The authors declare no conflicts of interest.
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