DFT Studies of NH–Cl Hydrogen Bond of Amino Acid Hydrochloride Salts in Ion Channels

Quantum chemical calculations were made, to study NH–Cl hydrogen bonds of two amino acid hydrochloride salts called alanine and threonine. The Nuclear Magnetic Resonance and Nuclear Quadrupole Resonance parameters for nitrogen and chlorine were calculated via four functionals such as, B3LYP, M062X, M06L, and CAM-B3LYP and by applying the 6-311++G(d,p) basis set. One of the functionals produced more accurate results. Geometry optimization was performed using the M062X/6-31++G(d,p) method, and Natural Bond Orbitals analysis was performed by applying the M062X/6-311++G(d,p) level. This study examined Nuclear Magnetic Resonance and Nuclear Quadrupole Resonance parameters with changes in structure from monomer to pentamer and investigated correlations between Natural Bond Orbitals parameters and Nuclear Magnetic Resonance or Nuclear Quadrupole Resonance parameters. The Natural Bond Orbitals parameters were used to investigate changes in structural parameters along with crystal development.


Introduction
Properties of the hydrogen bond are well known because it has been the subject of many investigations. [1][2][3][4][5][6] Hydrogen bonds have an important role in biological systems 7 and in the determination of structures and properties of large molecules in biochemistry, chemistry, and materials science. [8][9][10][11][12] The detection of molecular structure in Ion Channels is possible by studying the hydrogen bonds. Amino acids are components of ion channels. These channels that are located in cell membranes guide electrical current through the membrane. [13][14][15] Ion channels play a major role in biological processes and when defective can cause significant health problems such as Bartter's syndrome, cystic fibrosis, startle disease, and myotonia. 13 For example, a defect in alanine, histidine, threonine, aspartic acid, and cysteine amino acids leads to mutation or change in CLCNKB a ion channel that causes type III of Bartter's syndrome. 16 Thus, the study of the structural and binding environments of inorganic atoms within these channels has important implications. The knowledge of the structure of these channels can be increased by studying the hydrogen bonds. Thus, the aim of the study of interactions in amino acids is to determine any change in structure to recognize any defects in these channels. Most information regarding the structure of ion channels has been obtained by X-ray crystallography, 17,18 but in this study, the goal is to evaluate any changes in the structure of these channels by using solid-state nuclear magnetic resonance (SSNMR) and nuclear quadrupole resonance (NQR). 19 In general, the study of biological molecules, such as proteins, use the NMR spectroscopy technique that is beneficial for determining structure in both the solution 20,21 and solid states. 22,23 Solid-state NMR has been considered a lot over the past several decades, 24,25 including studies on proteins, 26 polymers, inorganic materials, 27 as well as clays and minerals. 28 More accurate information can be obtained by using NQR data in addition to NMR data. 29 We can understand any changes in a The CLCNKB gene belongs to the CLC family of genes, which provide instructions for making chloride channels. These channels, which transport negatively charged chlorine atoms (chloride ions), play a key role in a cell's ability to generate and transmit electrical signals. Some CLC channels regulate the flow of chloride ions across cell membranes, while others transport chloride ions within cells.

NMR Tensor Convention
In SSNMR, we have to calculate chemical shielding tensor parameters to obtain information about interactions. In Haeberlen-Mehring-Spiess (HMS) convention, 33,34 three NMR parameters can be calculated by using three principal components of the chemical shielding tensor, σ XX , σ YY and σ ZZ . The relationship between three principal components of the chemical shielding tensor must always be as follows: |σ ZZ -σ iso |≥ |σ XX -σ iso |≥ |σ YY σ iso |. The NMR parameters defined below: where σ iso is the isotropic shielding value, Δσ is the shielding tensor anisotropy, and η is shielding tensor asymmetry, which must always have a value between zero and one.

2. Nuclear Electric Quadrupolar Interaction
Nuclei with nuclear spin quantum number (I) larger than 1/2, are quadrupolar nuclei. For these nuclei, the electric charge is not spherically symmetrical, and they have an electric quadrupole moment, Q. The electrostatic field gradient tensor (EFG) arising from the electron distribution, and it will couple with Q at the nuclear center, so these nuclei can be studied by NQR spectroscopy. Principal components of EFG tensor must be arranged in this way: q ZZ ≥ q YY ≥ q XX .
The quadrupolar coupling constant (C Q ) and the asymmetry parameter (η Q ), represent the magnitude of quadrupole interaction and the symmetry around the nucleus, respectively, where e is the charge on an electron, Q is the nuclear electric quadrupole moment, and h is Planck's constant: The other aim of this study was to show the correlation between the structural parameters and Natural Bond Orbitals (NBO) data. Analysis of the hydrogen bonding was required to achieve this goal. The A-H-B hydrogen bond is a combination of two effects: 35 (1) The hyperconjugative effect that decreases the strength of the A-H bond thereby increasing the length of the A-H bond. This effect is the electron charge transfer from the lone pair of the Lewis base, B, to the antibonding orbital, σ * , of the A-H bond. This interaction, n B → σ AH * , can be calculated as the second-order perturbation theory energy (Eq. (6)): 36 (6) where < n B |F|σ AH * > is the Fock matrix element, and ε(σ AH * )-ε(n B ) is the energy difference between these two orbitals. (2) The rehybridization effect that leads to an increase in A-H bond strength also decreases the A-H bond length. This effect is a concept of Bent's rule, which speaks to the hybridization of the central atom (A) in the molecule X-A-Y. A provides hybridized atomic orbitals that form A's part of its bond to X and to Y. Bent's rule says that as we change the electronegativity of X and/or Y, A will tend to rehybridize its orbitals such that more s character will be placed in those orbitals and be directed towards the more electropositive substituent. 37

Methods
Calculations of molecular orbital were carried out using the density functional theory (DFT) method. All DFT calculations were performed using the GAMESS electronic structure package. 38 Alanine hydrochloride atomic coordinates and unit cell parameters were derived from X-ray or neutron diffraction studies of Di Blasio et al., 39 while threonine hydrochloride atomic coordinates from the X-ray structures of L. Bryce et al. 25 were used. The geometry optimizations were performed using M06-2X method with 6-31++G(d,p) basis set to find the position of hydrogen atoms in the stable state of the system from monomer to pentamer in threonine hydrochloride ( Figure 1) and alanine hydrochloride ( Figure 2). Reports show that this method is more accurate for matching to experimental data. 30 The models closely approximate the real crystal. The study of large structures is not possible because of the limited capacity of computer systems. So in this study the addition of monomer units to the initial monomer were continued until pentamer because the NQR parameters approach a steady limit (see Tables 1-4). Calculations of the chlorine and nitrogen nuclear magnetic shielding and EFG tensors were based on these models and by using four functionals, B3LYP, M06-2X, M06L, CAM-B3LYP, and 6-311++G(d,p) basis set. The M06-2X/6-311++G(d,p) method was used for calculating NBO parameters.

1. Investigation of NQR Parameters
The models for amino acid hydrochloride salts, shown in Figures 1 and 2, were utilized in quantum chemical calculations of the NMR interaction tensors. Results presented in Tables 1-4 show that molecular interactions significantly affect the electric field and its gradient in these two hydrochloride clusters, and also indicate that the quadrupolar coupling constant of chlorine and nitrogen nuclei decrease from dimmer to pentamer in all functionals. Reduction in the C Q value is connotative of an increment in hydrogen bond strength. 40 According to Tables 2 and 4, a decrease in C Q in alanine hydrochloride salt is more significant than a decrease in C Q in another salt, which could be as a result of hydrogen bond forma-   tion. In an alanine hydrochloride salt, the nitrogen atom can contribute to hydrogen bonding with a chlorine atom of a neighboring molecule, but it is not possible for a nitrogen atom in the threonine hydrochloride salt, and it contributes to one hydrogen bond. So, we expected that all changes in NQR parameters were larger in an alanine hydrochloride salt. The asymmetry parameter (η Q ) can show the information about the symmetry of the nuclear environment. The asymmetry parameter of chlorine in both hydrochloride salts increases regularly, but for nitrogen atoms this parameter decreases from dimmer to pentamer. All changes were investigated from dimmer to pentamer, because the molecule is still in a gas phase rather than a crystalline state in a monomer situation. Consequently, we can use NMR and NQR parameters to evaluate any changes in the structure of amino acids, hence, we can determine any changes in the structure of ion channels.

2. Computational Errors
Usually the magnitude of C Q ( 35 Cl) measured from NMR spectra of chloride ions in organic and inorganic salts range from essentially zero in cubic salts to greater than 9.0 MHz, 41,42 and the results of the calculations of the chlorine-35 quadrupolar coupling constants measured in this study were in this range. According to available experimental data for chlorine nucleus, 25,43 we can compare four methods used for calculating NQR parameters in these two amino acids. By comparing the experimental and   Tables 1 and 3, the M06L/6-311++G(d,p) method is more accurate and has the lowest computational error for calculating C Q in these molecules. Figure 3 shows the average of errors calculated for two hydrochloride salts. According to available NMR experimental data for chlorine nuclei, 43 percent errors in calculating σ iso of the chlorine nucleus in alanine hydrochloride salt for B3LYP, M06-2X, M06L, CAM-B3LYP functional were 3.10%, 3.23%, 2.69%, and 4.71%, respectively, and for threonine hydrochloride were 12.74%, 15.32%, 11.82%, and 14.84%, respectively. So, we can see again that the M06L/6-311++G(d,p) method was the most accurate method in these two amino acids.

Correlation Between NMR and NBO Parameters
Changes in anisotropy parameter are correlated to the NBO parameters. Chemical shielding anisotropy of ni- Figure 5. Correlation between percent of P orbital and Δσ in threonine hydrochloride salt.

4. Analysis of Structural Parameters
In this study we have investigated NH-Cl hydrogen bond in crystal lattice. Two effects influence the A-H-B hydrogen bond: the hyperconjugative effect that decreases the strength of A-H bond and subsequently increases the length of the A-H bond, and the rehybridization effect that leads to an increase in the A-H bond strength that then decreases the A-H bond length. 44 The hyperconjugative effect is connected with the energy of electron charge transfer, E NBO , and will increase if this energy in- trogen atom in alanine hydrochloride decreases with increasing cluster size. According to Table 5, hybridization of nitrogen atom changes from SP 3.12 to SP 3.10 , this increase in s character and decrease in p character cause the electronic cloud around the nucleus to become more symmetric, and chemical shielding anisotropy subsequently decreases. Similarly, a nitrogen atom in threonine hydrochloride changes from SP 3.14 to SP 3.11 , so the symmetry around the nucleus increases, and the anisotropy parameter decreases, as shown in Tables 4 and 6, and Figures 4 and 5.  creases. The s-character of the A-atom hybrid orbital in the A-H bond is directly dependent to the rehybridization process. The structural parameters for alanine hydrochloride are presented in Table 7. According to Table 5

Conclusions
The EFG and the chemical shielding tensors have been calculated for chlorine and nitrogen nuclei, via the following four functionals: B3LYP, M062X, M06L, and CAMB3LYP and with 6-311++G(d,p) basis set. The aim of this study was to demonstrate the sensitivity of NMR interaction tensors to slight differences in the local environment at every nucleus where there was a NH-Cl hydrogen bond. This matter is so crucial because it illustrates the changes in ion channel structure, whereby the NMR and NQR parameters are significantly changed when the structures of the monomer transform to pentamer. The results agree with experimental data, which illustrates that the M06L/6-311++G(d,p) method is the most accurate method for NMR and NQR calculations in these two amino acids. In addition, it is shown that there was a high correlation between NMR parameters and NBO parameters, and between structural parameters and NBO parameters.
Information from NMR, NQR, and NBO analysis are useful for interpretation of the structure in both solu-  tion and solid states. These techniques are especially useful for biological molecules such as proteins and also for larger systems with unknown structure.