A comparative study of the low-frequency vibrations of L-histidine molecule in different solid states
Li Xu a, Yin Li b,⁎, Qi Zhou b, Xiaohua Deng b,c
a Department of Chemical Engineering and Technology, School of Chemistry, Biology and Materials Science, East China University of Technology, Guanglan Avenue 418, Nanchang City 330013, China
b Department of Physics, School of Sciences, Nanchang University, Xuefu Avenue 999, Nanchang City 330031, China
c Institute of Space Science and Technology, Nanchang University, Xuefu Avenue 999, Nanchang City 330031, China
a b s t r a c t
Low-frequency vibrations of L-histidine in a neat solid state and its monohydrochloride monohydrate are both investigated using THz spectroscopy and DFT calculations. The molecular motions in those modes are further quantitatively decomposed into a number of submotions and discussed in terms of their contributions to a mode. The results show significant differences in the averaged contribution percentage of intermolecular mo- tions and the dihedral angle distortions of the imidazole ring between these two crystals. Those phenomena are interpreted from the viewpoint of their hydrogen-bond configurations.
Keywords:
Terahertz spectroscopy DFT calculation
Low-frequency vibrations
L-Histidine
L-Histidine monohydrochloride monohydrate
1. Introduction
Low-frequency vibrations play significant roles in the property and function of biomolecules. They have been verified to be related with conformational change [1], binding interaction [2], and solvation [3]. Unveiling the nature of such motions is beneficial to improving the un- derstanding of many biological processes. Since these vibrations take place at terahertz (THz) frequency region, THz spectroscopy is regarded as a useful technique. In the past two decades, THz spectroscopic studies on the low-frequency vibrations of biomolecule in solid-state and aque- ous phase have been extensively reported [4–9]. The mechanisms of low-frequency vibrations in biological property and function have been gradually clarified.
Amino acids are one kind of target compounds in the field of vibra- tional spectroscopy due to their significant roles in life science. The fea- tures of their low-frequency vibration have been revealed using far-IR spectroscopy [10,11]. The development of THz spectroscopy further fa- cilitates the access to their low-frequency vibrations, unveiling the na- ture of those motions in biological processes [12,13]. It is well known that intermolecular interactions, especially hydrogen bonds, are greatly associated with the functions of amino acids. However, how hydrogen bonds affect the features of low-frequency vibrations is rarely reported. This may be due to the complexity of low-frequency vibrations, which involve both inter and intramolecular motions.
Several efforts have been made to analyze low-frequency vibrations. Jepsen and coworkers [14]first proposed a quantitative approach to sep- arate the contributions from inter and intramolecular components in a vibrational mode. Then, librational motion was further introduced into this model as an independent component [15,16]. Schmuttenmaer and coworkers [17] proposed a sophisticated method which is capable of quantitatively decomposing one vibrational mode into four catego- ries including translational motions, librational motions, bond angle and dihedral angle distortions, and further projecting it into a number of submotions. This method provides a clear picture showing the inten- sity of every submotion in one vibrational mode. Therefore, it becomes a useful tool for analyzing low-frequency vibrations [18–20].
In this work, with the aim to clarify how hydrogen bonds impact on the feature of low-frequency vibration for an amino acid molecule, we studied the vibrations in THz range of L-histidine in a neat solid state (orthorhombic form) and its monohydrochloride monohydrate (L- histidine·HCl·H2O). Their molecular structures and unit cells are shown in Figs. 1 and 2, respectively. By using a modified Schmuttenmaer’s method, we quantitatively compared the difference in molecular motions of L-histidine between these two forms, and gave interpretations from the viewpoint of hydrogen-bond configuration.
2. Experimental
2.1. Materials
L-Histidine (purity N99%), L-histidine·HCl·H2O (purity N99%) and polyethylene (particle size: 40–48 μm) were all purchased from Sigma-Aldrich corporation. They were directly used without further purification.
Sample pellets need to be prepared prior to THz absorption mea- surement. A desired amount of amino acid was first sufficiently mixed with polyethylene powder in an agate mortar by grinding with a pestle. Then they were transferred into a 13 mm evacuable pellet die. Sample powder were finally pressed into a pellet with a thickness of 1.0–1.4 mm by using a hydraulic press.
2.2. Experimental method
Time-domain terahertz spectrometer (Batop TDS1008, Germany) was employed to acquire THz absorption signals of reference and samples. This device utilizes a femto-second laser source to illumi- nate photo-conductive antennas for THz pulse generation and detec- tion. The measurements were conducted in transmission configuration. Prior to every measurement, dry nitrogen gas was purged into sample compartment to reduce the influence from water vapor in air. Reference and sample signals were recorded without and with sample pellet in THz beam path, respectively. The time resolution was set to 0.05 ps. The total time for each measurement was set to 20 ps. Recorded time-domain signals were further converted into frequency-domain spectra with FFT algo- rithm. Absorption spectra were calculated via comparison between reference and sample signals in frequency-domain.
2.3. Computational method
Theoretical calculations were carried out using Quantum Espresso (QE) package [21] and Phonopy code [22]. Geometry optimization was first performed using PWscf code with PBE functional plus Grimme’s D2 correction term [23]. Both cell parameters and atomic po- sitions were allowed to relax. The convergence criterion of optimal ge- ometry based on total energy and force were 1.0 × 10−5 Ry and 5.0 × 10−6 Ry/au, respectively. Ultrasoft pseudopotentials were used to describe electron-ionic core interactions. The planewave cutoff energy and kinetic cutoff energy for charge density were 60 Ry and 600 Ry, respec- tively. Monkhorst-Pack k-point samplings were generated with a 4 × 3 × 1 grid for L-histidine and a 1 × 2 × 3 grid for L-histidine·HCl·H2O, re- spectively. All the DFT calculations were carried out on a high- performance computing system located at Institute of Space Science and Technology in Nanchang University.
Phonopy code was utilized to obtain vibrational modes based on fi- nite displacement method. Intensity of vibrational mode was calculated using the equation proposed by Fernández-Torre and coworkers [24]. Details can be found in our previous work [9,19].
3. Results & discussion
3.1. Experimental THz absorption spectra
The measured THz absorption spectra of L-histidine and L- histidine·HCl·H2O are shown in Fig. 3. The original time-domain signals are provided in Figs. S1 and S2 of Supplementary Material. THz absorp- tion spectrum of L-histidine reveals four absorption peaks centered at 0.78, 1.71, 2.02 and 2.41 THz. Under our condition, absorption peaks (marked with asterisk in Fig. 3) above 2.3 THz have large uncertainty due to the low signal-noise ratio. With reference to the THz spectra of
L-histidine in the orthorhombic form measured by Schmuttenmaer and coworkers [25], our observation is consistent with the reported spectrum. The THz spectrum of L-histidine·HCl·H2O shows two peaks below 2.0 THz. They center at the positions of 0.90 and 1.64 THz which are similar to the peaks featured below 2.0 THz in the spectrum of L-histidine. Moreover, two peaks at 2.19 and 2.44 THz can be ob- served. Our observation in the spectrum of L-histidine·HCl·H2O are almost the same with that observed by Zhao and coworkers [26] except for slight position shifts above 2.0 THz.
As both L-histidine and L-histidine·HCl·H2O crystals exist in ortho- rhombic form, the sizes of their unit cells are close to each other, this triggers our curiosity in exploring their low-frequency vibrations to see whether these modes show any similarity between these two crys- tals. Hence, we further carried out geometry optimizations followed by phonon calculations using DFT approach.
3.2. Calculated THz absorption spectra
Prior to calculating phonons of L-histidine and its monohydrochloride monohydrate crystals, we first carried out geome- try optimizations using the experimental structures deposited in the Cambridge Crystallographic Data Centre as initial geometries. The crys- tal structure files with Identifier: LHISTD13 [27] and HISTCM12 [28] were employed for L-histidine and L-histidine monohydrochloride monohydrate, respectively. And they were converted into PWscf input files with settings mentioned in Section 2.3. Geometry optimizations successfully achieved convergence for both crystals. Their initial and op- timized geometries are compared in Table 1.
As can be seen from Table 1, for both crystals, the angles of the ortho- rhombic form are kept, but the volume of unit cell is underestimated by 3–5%. This is mainly due to the shortening of one edge length of their unit cells. As Fig. 2 shows, the lines along the most underestimated unit cell length, namely b in L-histidine and a in L-histidine·HCl·H2O, are both approximately perpendicular to the plane of imidazole ring. This may indicate DFT calculations tend to shorten the distance between stacked L-histidine molecules. Or it can also be resulted from the fact the experimental structures were obtained in a temperature above 0 K, in which anharmonicity effect cannot be neglectable.
3.3. Analyses of characters of the low-frequency modes
Characters of the low-frequency modes were quantitatively ana- lyzed based on the principle of Schmuttenmaer’s method with some modifications. Briefly speaking, according to the atomic displacement vectors in a vibrational mode, molecular motion is first decomposed into three categories including translational motion, librational motion and intramolecular distortion. The contribution percentage of each cat- egory is calculated according to the equations described in our previous work [9]. Secondly, each category is further divided into several submotions. Translational motions are decomposed into three transla- tions along x, y and z axes. And librational motions can be regarded as the combination of librations around the three principal axes Ra, Rb and Rc of molecule. Moments of inertia and orientations of the principal axes are provided in Tables S1 and S2 of Supplementary Material. Intra- molecular distortions are decomposed into bond angle distortions and dihedral angle distortions. Equations of all above procedures are elabo- rated in our previous work [9,19]. The results of quantitative analysis are finally depicted in stripes, as shown in Figs. 5 and 6. The color intensity represents the amplitude or contribution of the corresponding submotion to one mode. The red and blue colors represent positive and negative changes, respectively.
In order to compare the vibrational motions of L-histidine molecule in its neat form and in the form of L-histidine·HCl·H2O, the normaliza- tion is only implemented on L-histidine molecule itself, ignoring the motions from HCl and H2O molecules. This treatment ensures that ei- ther in L-histidine neat form or in the form of L-histidine·HCl·H2O, the sum of total contribution percentages from translational and librational motions, and intramolecular distortions of L-histidine molecule itself is equal to 1, allowing us to compare two crystals with each other.
We first pay our attentions to those modes which cause absorption in our spectral range. As Fig. 5 reveals, the absorption peak at 0.78 THz of L-histidine, which arises from the mode 4, involve a translation along x axis, a libration mainly around an axis between Rb and Rc, bond angle distortions taking place mainly at imidazole ring, and dihe- dral angle distortions taking place at imidazole ring, carboxylic and amino groups. In Fig. 6, the stripe pattern of L-histidine in the mode 4 suggests L-histidine molecule vibrates in a different way, especially in the aspect of intramolecular distortions. In case of L-histidine·HCl·H2O, there is no significant bond angle distortion occurring, and the dihedral angle distortions mainly take place in the carboxylic and amino groups. In Fig. 4a, the mode 9 and mode 11 in crystal of L-histidine are as- cribed to the origins of the absorption peaks at 1.71 and 2.02 THz, re- spectively. Fig. 5 shows that the mode 9 involves both bond angle distortions and the dihedral distortions nearly around the whole mole- cule, and the mode 11 mainly involves large dihedral distortions in the carboxylic group, amino group and the aliphatic moiety of the side chain of L-histidine. In the L-histidine·HCl·H2O, the modes 8 and 9, 16 and 17, which correspond to absorption peaks at 1.64, 2.02 and 2.44 THz, re- spectively, show different characters from the mode 9 and 11 of L- histidine crystal. In contrast to the intensity of bond angle distortions of the mode 9 of L-histidine crystal, neither the mode 8 nor 9 shows ob- vious bond angle distortion. Moreover, the dihedral angle distortions of the imidazole ring are much weaker than those in L-histidine. And it is can be easily recognized that the dihedral angle distortions of the imid- azole ring in all of the studied low-frequency vibrations in L- histidine·HCl·H2O are much weaker compared to those in L-histidine. In the mode 16 of L-histidine·HCl·H2O, the dihedral angle distortions take place mainly in the carboxylic group and amino group, and slightly involve the side chain. Like the mode 16, the mode 17 shows a similar feature in dihedral angle distortions, but its most intensive distortions take place in main chain and amino group. Compared with mode 16 and 17, the dihedral angle distortions of the mode 11 in L-histidine crys- tal occur in the same part of L-histidine molecule, but their intensities are prominently higher than that of the mode 16 and 17.
In order to gain a statistical view on the low-frequency modes, we average the contribution percentages of translation, libration, bond angle distortion and dihedral angle distortion of the first 20 low- frequency modes excluding three acoustic modes. These results are summarized in Table 2. The large difference between L-histidine and L- histidine·HCl·H2O can be easily recognized in terms of translation and dihedral angle distortion. The averaged contribution percentage of translational motions of L-histidine is about 15% lower than that of L- histidine·HCl·H2O. While its averaged contribution percentage of dihe- dral angle distortions is about 9% larger than the counterpart of L- histidine·HCl·H2O.
Since the intermolecular motions of molecule are associated with noncovalent interactions within crystal, we simply calculated the bind- ing energies among molecules within these two crystals using the fol- lowing equation Ebinding ¼ Ecrystal− n1 · Ecomponent1;gas þ n2 · Ecomponent2;gas þ … where Ebinding is the binding energy of molecules in the crystal; n1,2,..is the number of constituent molecules in a unit cell; Ecomponent1, 2, …, gas are their electronic energies, which were obtained by centering a single molecule into a 25 Å × 25 Å × 25 Å cubic box followed by geometry op- timization. As the contributions from zero-point energy and thermal property are usually relatively small, we just only took electronic contri- butions into account. The results are provided in Table 3.
As Table 3 reveals, the binding energy of L-histidine·HCl·H2O is−389.554 kJ/mol, which is substantially higher than that of L-histidine. This is rational as the presence of HCl and H2O in L-histidine·HCl·H2O produces stronger hydrogen bonding networks. As a consequence, the strength of non-covalent interactions in L-histidine·HCl·H2O is much higher than in L-histidine. This can be regarded as the dominant factor governing intermolecular motions in these two crystals. And the stron- ger non-covalent interactions are, the more intensive intermolecular motions are induced.
Attentions are also need to be paid on the intramolecular motions. As Figs. 5 and 6 show, a prominent difference between two crystals in terms of intramolecular motions is that dihedral angle distortions of imidazole ring in L-histidine are more intensive than in L- histidine·HCl·H2O. This phenomenon can be attributed to the orienta- tion of the hydrogen bonds linked to imidazole ring. As drawn in Fig. 2a, in L-histidine, although the intermolecular hydrogen bonds (red dash lines) linked to imidazole ring stay in the same plane with im- idazole ring, the intramolecular hydrogen bonds (cyan dash lines) shows an angle of about 30 degree with the plane of imidazole ring, which is able to initiate out-of-plane motions. In L-histidine·HCl·H2O shown in Fig. 2b, all the hydrogen bonds linked to imidazole ring are nearly in the same plane of imidazole ring, mainly leading to in-plane motions. Hence, the orientation difference of hydrogen bonds could be considered as the cause which gives rise to different dihedral angle dis- tortion of imidazole ring between two crystals.
4. Conclusions
We have studied the characters of low-frequency motions of L- histidine in a neat solid state (orthorhombic form) and its monohydrochloride monohydrate using THz spectroscopy and DFT cal- culations. Although the experimental spectra of two crystals show sim- ilarity with each other to some extent in our spectral range, the characters of their vibrational modes are very different. The quantitative analyses on the vibrational modes suggest the contribution from inter- molecular motion to low-frequency vibration in L-histidine·HCl·H2O is much larger than in L-histidine. This result is attributed to their different binding L-Histidine monohydrochloride monohydrate energies among molecules within crystal. Furthermore, in terms of intramolecular motion, the distortion of imidazole ring in L- histidine·HCl·H2O is less intensive than in L-histidine. This could be as- cribed to the orientation of hydrogen bonds linked to the imidazole ring.
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