Novel Tautomerisation Mechanisms of the Biologically Important Conformers of the Reverse Löwdin, Hoogsteen, and Reverse Hoogsteen G*·C* DNA Base Pairs via Proton Transfer: A Quantum-Mechanical Survey

Introduction

The study of the tautomerization mechanisms of the hydrogen (H) bonded nucleotide base pair is an important topic of modern quantum biophysics, biochemistry, molecular, and structural biology (Sinden, 1994; Sponer and Lankas, 2006; Alkorta et al., 2018). For over 65 years, this area of research has been under the intense scrutiny of both theoretics and experimentators, since the establishment of the spatial organization of DNA and formulation of the so-called “tautomeric hypothesis of the origin of spontaneous point mutations (transitions and transversions)” (Watson and Crick, 1953a,b; Erdmann et al., 2014) for this biologically important macromolecule—carrier of the genetic information, which is transmitted from generation to generation.

Lately, this tautomeric hypothesis has been experiencing an era of renaissance (Brovarets' and Hovorun, 2018). Thus, for the first time, within the framework of this hypothesis the new structural mechanisms of the tautomerization of pairs of nucleotide bases have been discovered, in which the transition of bases within the base pair into the mutagenic tautomeric form is accompanied by a significant change in the geometry of the base pair itself (Brovarets' and Hovorun, 2009, 2015a,b,c,d,e, 2016, 2018).

However, at the studying of the nature of the mutagenic tautomerization of DNA bases, the researchers limited themselves to the A·T and G·C Watson-Crick base pairs (Löwdin, 1963, 1966; Florian et al., 1994; Gorb et al., 2004; Bertran et al., 2006; Brovarets' and Hovorun, 2014a,b). Now this problem is considered more complex with the involvement of several biologically important conformers of these pairs (Hoogsteen, 1963; Pous et al., 2008; Alvey et al., 2014; Brovarets' and Hovorun, 2014a,b; Nikolova et al., 2014; Acosta-Reyes et al., 2015; Poltev et al., 2016; Zhou, 2016; Szabat and Kierzek, 2017; Ye et al., 2017).

These observations do not only allow to penetrate deeper into the essence of the phenomenon being studied, but also to answer, in particular, on a biologically important question—“Why Nature has exactly chosen the Watson-Crick DNA base pairs as elementary structural units for the construction of genetic material?”

Nowadays, there is an explicit bias to the A·T DNA base pair at the investigations of this type. This is due to a large number of circumstances, which will be outlined and discussed below.

Thus, it is widely known that the classical A·T(WC) Watson-Crick DNA base pair (Brovarets' and Hovorun, 2014b) may acquire different biologically significant conformations with various organization of the three intermolecular H-bonds—reverse Watson-Crick A·T(rWC), Hoogsteen A·T(H), and reverse Hoogsteen A·T(rH), which have been comprehensively studied in the literature (Hoogsteen, 1963; Pous et al., 2008; Alvey et al., 2014; Brovarets' and Hovorun, 2014b; Nikolova et al., 2014; Acosta-Reyes et al., 2015; Poltev et al., 2016; Zhou, 2016; Szabat and Kierzek, 2017; Ye et al., 2017).

Thus, in particular, in previous works (Hoogsteen, 1963; Pous et al., 2008; Brovarets' and Hovorun, 2010, 2014b, 2015f; Brovarets', 2013a,b; Alvey et al., 2014; Nikolova et al., 2014; Acosta-Reyes et al., 2015; Poltev et al., 2016; Zhou, 2016; Szabat and Kierzek, 2017; Ye et al., 2017; Brovarets' et al., 2018a,b,c,d,e,f; Brovarets' and Tsiupa, 2019) by the methods of quantum chemistry we have investigated in details the potential (electronic) energy surface of each of the four biologically important A·T DNA base pairs—Watson-Crick A·T(WC), reverse Watson-Crick A·T(rWC), Hoogsteen A·T(H) and reverse Hoogsteen A·T(rH), leading to the novel conformational or tautomeric states of these base pairs. It was theoretically demonstrated that these A·T(WC/rWC/H/rH) base pairs possess unique ability to perform conformationally-tautomeric transition into the planar wobble A*·T(w), A·${\text{T}}_{\text{O}2}^{*}$(w), and A·T*(w) base mispairs, non-planar wobble A·T(w_WC), A·T(w_rWC), A·T(w_H), and A·T(w_rH) base mispairs and incorrect A·T*(${\text{w}}_{\text{WC}}^{\perp }$), A·${\text{T}}_{\text{O}2}^{*}$(${\text{w}}_{\text{rWC}}^{\perp }$), A·T*(${\text{w}}_{\text{H}}^{\perp }$), and A·${\text{T}}_{\text{O}2}^{*}$(${\text{w}}_{\text{rH}}^{\perp }$) base mispairs containing mutagenic tautomers of the DNA bases, and also their interconversions between each other through the non-planar transition states via the structural or conformational rearrangements and intramolecular proton transfer along the intermolecular H-bonds.

In contrast to this, the classical G·C Watson-Crick DNA base pair (Brovarets', 2013b; Brovarets' and Hovorun, 2014a, 2015f) could not acquire different conformations in the main tautomeric state due to the obstacles presented by its geometrical structure. This, however, can be overcome through the G·C(WC) → G*·C*(WC) tautomerisation via the double proton transfer (DPT), according to Löwdin's mechanism (Löwdin, 1963, 1966; Brovarets' and Hovorun, 2014a, 2018). This Löwdin's reaction can proceed over the barrier of tautomerization or under the barrier via the tunneling (Parker and Van Everv, 1971; Boutis, 1992; Al-Khalili and McFadden, 2014; Brovarets' and Hovorun, 2015g; Godbeer et al., 2015; Turaeva and Brown-Kennerly, 2015; Meisner and Kastner, 2016; Roßbach and Ochsenfeld, 2017; McFadden and Al-Khalili, 2018; Pusuluk et al., 2018; Smedarchina et al., 2018; Shekaari and Jafari, 2019; Srivastava, 2019).

At this, the so-called Löwdin G*·C*(WC) base pair with geometry close to Watson-Crick, which is created in such a way, involving mutagenic tautomers of the DNA bases, can acquire similarly to the A·T(WC) base pair different conformations (Brovarets' and Hovorun, 2010, 2015f; Brovarets', 2013a,b; Brovarets' et al., 2018a,b,c,d,e,f; Brovarets' and Tsiupa, 2019)—reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H) and reverse Hoogsteen G*′·C*(rH) (Brovarets', 2013b) (here and below the superscript “*” denotes the rare tautomeric form of the DNA base (Glushenkov and Hovorun, 2016) and “′”—trans-orientation of the OH group). This demonstrates quite unexpected role of the Löwdin's tautomerisation for the conformational variety.

Currently, there is no mention of reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H) and reverse Hoogsteen G*′·C*(rH) conformers or their tautomerisation via the DPT along the intermolecular H-bonds, despite a great number of investigations devoted to this important phenomenon.

In our previous studies we have comperehensively investigated the tautomerisation via the DPT of the canonical A·T(WC) (Brovarets' and Hovorun, 2014b, 2015g) and G·C(WC) (Brovarets' and Hovorun, 2014a) Watson-Crick DNA base pairs, and also of the incorrect DNA base pairs—wobble G·T base pair (Brovarets' et al., 2015), short C·T (Brovarets' and Hovorun, 2013a), C*·C (Brovarets' and Hovorun, 2013b), T*·T (Brovarets' et al., 2014a), H·C (Brovarets' and Hovorun, 2013c; Brovarets' et al., 2013a) and H*·T (Brovarets' and Hovorun, 2013c; Brovarets' et al., 2013a); long A·A* (Brovarets' and Hovorun, 2013d), A·G (Brovarets' et al., 2014b), G·G* (Brovarets' and Hovorun, 2014c), H·H (Brovarets' and Hovorun, 2013c; Brovarets' et al., 2013a), H*·H (Brovarets' and Hovorun, 2013c; Brovarets' et al., 2013b) and H·A (Brovarets' and Hovorun, 2013c; Brovarets' et al., 2014c); Watson-Crick-like A·C* (Brovarets' and Hovorun, 2015h), G*·T (Brovarets' and Hovorun, 2015i), G·A_syn (Brovarets' and Hovorun, 2014d), A*·${\text{G}}_{\text{syn}}^{*}$ (Brovarets' and Hovorun, 2014d), A*·A_syn (Brovarets' et al., 2014d), G·${\text{G}}_{\text{syn}}^{*}$ (Brovarets' and Hovorun, 2014e), T·2AP*(w) (Brovarets' et al., 2017; Brovarets' and Hovorun, 2019a), and G·2AP*(w) (Brovarets' et al., 2017; Brovarets' and Hovorun, 2019a) base mispairs and protein-DNA complexes (Brovarets' et al., 2012), which we have summarized in our review (Brovarets' and Hovorun, 2019b), devoted to the microstructural mechanisms of the tautomerization by the proton transfer along the neighboring intermolecular H-bonds in 22 biologically important pairs of nucleotide bases in the framework of the author's method, which enable to trace the evolution of the physico-chemical parameters along the intrinsic reaction coordinate (IRC).

In this study, we aim to reapply the approach, which we launched in our previous works (Brovarets' et al., 2018a,b,c,d,e,f; Brovarets' and Tsiupa, 2019) in order to investigate in details the tautomerisation of the reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H), and reverse Hoogsteen G*′·C*(rH) base pairs via PT along the neighboring intermolecular H-bonds.

As a result of the previous investigations, it was established that proton mobility along the intermolecular H-bonds does not change the tautomeric status of the investigated base pairs. Along with this biologically important conclusion, for the first time we have obtained a number of important physical and chemical characteristics. As such, it was documented that tautomerisation of the reverse Löwdin G*·C*(rWC) DNA base pair along the middle H-bond induces analogous SPT along its upper and lower H-bonds. Moreover, for the first time we have described the formation of a dynamically stable base pair with participation of the yilidic form of the purine base, formed through asynchronous DPT and participation of the CH group as proton donor.

Digging deeper into the mechanisms of tautomerisation of the reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H), and reverse Hoogsteen G*′·C*(rH) base pairs, we have carefully obtained sweeps of the physical and chemical parameters that characterize proton mobility along the IRC. Firstly, we have established a monotonic dependence of the base pair's dipole moment along the IRC. Second, it was shown that the SPT processes are characterized by the presence of 6 key points.

Computational Methods

Density Functional Theory Geometry and Vibrational Frequencies Calculations

All calculations of the geometries and harmonic vibrational frequencies of the considered base mispairs and transition states of their conversion have been conducted using Gaussian'09 package (Frisch et al., 2010) at the DFT B3LYP/6-311++G(d,p) level of theory (Lee et al., 1988; Parr and Yang, 1989; Tirado-Rives and Jorgensen, 2008), that has been already applied for analogous systems and approved to give accurate geometrical structures, normal mode frequencies, barrier heights, and characteristics of intermolecular H-bonds (Matta, 2010; Arabi and Matta, 2018; Gatti et al., 2018). We have used a scaling factor equal to 0.9668 in order to correct harmonic frequencies for the investigated base pairs (Brovarets' and Hovorun, 2010, 2015f; Brovarets', 2013a,b; Palafox, 2014; El-Sayed et al., 2015; Brovarets' et al., 2018a,b,c,d,e,f; Brovarets' and Tsiupa, 2019). We have associated structures, which were localized on the potential energy landscape by means of Synchronous Transit-guided Quasi-Newton method (Peng et al., 1996), to the minima or transition state (TS) by the absence or presence of the imaginary frequency in the vibrational spectra of the complexes, respectively. We used standard TS theory (Atkins, 1998) in order to estimate the forward and reverse barriers of the investigated tautomerisation reaction.

IRC Calculations

Reaction pathways have been monitored by following IRC in the forward and reverse directions from each TS using Hessian-based predictor-corrector algorithm for integration (Hratchian and Schlegel, 2005). In such a way we ensure that it was received proper reaction pathway from reactants to products. Further, we have obtained the sweeps of the energetic, polar, and geometric characteristics of the H-bonds and base pairs along the IRC by calculating them at each point of the IRC (Brovarets' et al., 2017, 2018g,h).

Single Point Energy Calculations

In order to take into account electronic correlation effects, we followed geometry optimizations with single point energy calculations using MP2 level of theory (Frisch et al., 1990) and 6-311++G(2df,pd) Pople's basis set of valence triple-ζ quality (Hariharan and Pople, 1973; Krishnan et al., 1980) and aug-cc-pVDZ Dunning's cc-type basis set (Kendall et al., 1992), augmented with polarization and/or diffuse function.

The Gibbs free energy G for all structures was calculated by the formula:

$\begin{array}{ll}\begin{array}{c}\text{G}={\text{E}}_{\text{el}}{\text{+E}}_{\text{corr}},\end{array}& (1)\end{array}$

where E_el–electronic energy, while E_corr–thermal correction.

Interaction Energies Calculations

We have obtained electronic interaction energies E_int at the MP2/6-311++G(2df,pd) level of theory as the difference between the total electronic energy of the base mispair and the electronic energies of the separate monomers. Gibbs free energy of interaction has been obtained using similar approach. At this, we also corrected the interaction energy for the basis set superposition error (BSSE) (Boys and Bernardi, 1970; Gutowski et al., 1986) according to the counterpoise procedure (Sordo et al., 1988; Sordo, 2001).

Estimation of Kinetic Parameters

The time τ_99.9% spent for reaching the 99.9% of the equilibrium concentration between the initial and terminal base pairs in the system of reversible first-order forward (k_f) and reverse (k_r) reactions was estimated by formula (Atkins, 1998):

$\begin{array}{ll}{\tau }_{99.9\%}=\frac{ln{10}^3}{k_f+k_r},& (2)\end{array}$

The lifetime τ of the base pairs was calculated using the formula 1/k_r, where the values of the reverse k_r and forward k_f rate constants for the tautomerisation reactions were calculated as (Atkins, 1998):

$\begin{array}{ll}{k}_{f,r}=\Gamma ·\frac{k_{B}T}{h}{e}^{-\frac{\Delta \Delta G_{f,r}}{RT}},& (3)\end{array}$

where quantum tunneling effects are accounted by Wigner's tunneling correction (Wigner, 1932; Brovarets' and Hovorun, 2014d), that has been successfully used for the DPT reactions (Brovarets' and Hovorun, 2013a,b,c,d, 2014c,d,e, 2015h,i; Brovarets' et al., 2013a,b, 2014a,b,c,d, 2015, 2017):

$\begin{array}{ll}\Gamma =1+\frac{1}{24}{\left(\frac{h{\nu }_i}{k_{B}T}\right)}^2,& (4)\end{array}$

where k_B—Boltzmann's constant, h—Planck's constant, ΔΔG_f,r—Gibbs free energy for the forward (f) and reverse (r) tautomerisation reactions, ν_i—value of the imaginary frequency at the TS of the tautomerisation reaction.

QTAIM Analysis

Bader's quantum theory of Atoms in Molecules (QTAIM) was used to analyse the electron density distribution (Bader, 1990). The topology of the electron density was analyzed using program package AIMAll (Keith, 2010) with all default options and wave functions obtained at the level of theory used for geometry optimisation. The presence of the (3,−1) bond critical point (BCP), bond path between hydrogen donor and acceptor and positive value of the Laplacian at this BCP (Δρ >0) were considered altogether as criteria for the H-bond formation (Matta and Hernández-Trujillo, 2003; Matta et al., 2006a,b; Matta, 2014; Lecomte et al., 2015; Brovarets' and Pérez-Sánchez, 2016, 2017; Brovarets' et al., 2016).

Energies of the Intermolecular H-Bonds

We calculated the energies of the intermolecular AH···B H-bonds in the base mispairs and TSs and of the sweeps of the H-bond energies by the empirical Espinosa-Molins-Lecomte (EML) formula (Espinosa et al., 1998; Matta et al., 2006b; Mata et al., 2011; Lecomte et al., 2015; Alkorta et al., 2016, 2017) based on the electron density distribution at the (3,−1) BCPs of the H-bonds:

$\begin{array}{ll}{E}_{AH···B}=0.5·\text{V(r)},& (5)\end{array}$

where V(r)—value of a local potential energy at the (3,−1) BCP.

EML fomula has been also used for the estimation of the energy of the non-standard H-bonds CH···O in the stationary points of the base pairs on the hypersurface of their electronic energy.

We evaluated the energies of the classical NH···N/O and OH···O/N intermolecular AH···B H-bonds by the empirical Iogansen's formula (Iogansen, 1999):

$\begin{array}{ll}{E}_{AH\dots B}=0.33\sqrt{\Delta v-40},& (6)\end{array}$

where Δν–magnitude of the frequency shift of the stretching mode of the AH H-bonded group involved in the AH···B H-bond relatively the unbound group. We applied partial deuteration in order to minimize the effect of vibrational resonances (Brovarets' and Hovorun, 2014d,e, 2015h,i; Brovarets' et al., 2014d).

The energies of the NH···N and OH···O H-bonds in the TSs containing loosened covalent bridges were calculated by the Nikolaienko-Bulavin-Hovorun formula (Nikolaienko et al., 2012):

$\begin{array}{ll}{E}_{NH···N}=-2.03+225·\rho ,& (7)\end{array}$

$\begin{array}{ll}{E}_{OH···O}=-3.09+239·\rho ,& (8)\end{array}$

where ρ–the electron density at the (3,−1) BCP of the H-bond.

The atom numbering scheme for the DNA bases is conventional (Saenger, 1984).

Results and Their Discussion

In this paper we have investigated in details the tautomerisation processes via the single (SPT) or double (DPT) proton transfer of the G*·C*(rWC), G*′·C*(H), and G*′·C*(rH) base pairs along the neighboring intermolecular H-bonds as their intrinsically inherent property (Figure 1).

FIGURE 1

Figure 1. Discovered new reaction pathways of the tautomerization in the reverse Watson-Crick G*·C*(rWC) – I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·C*_O2(rWC), II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G*_N2·C(rWC), III. G*·C*(rWC)↔G*′_N2·C(rWC), Hoogsteen G*′·C*(H) – IV. G*′·C*(H)↔G*_N7·C(H)—and reverse Hoogsteen G*′·C*(rH) – V. G*′·C*(rH)↔G*′_N7·C(rH) – DNA base pairs through the single or double proton transfer. Electronic ΔE_int and Gibbs free ΔG_int energies of the interaction [MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory, in kcal·mol⁻¹], relative Gibbs free energies ΔG, and electronic energies ΔE [MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1 at T = 298.15 in kcal·mol⁻¹] are presented below complexes in brackets. Dotted lines indicate AH···B H-bonds – their lengths H···B are presented in angstroms; carbon atoms are in light-blue, nitrogen—in dark-blue, hydrogen—in gray and oxygen – in red. ν_i—imaginary frequencies at the TSs of the tautomeric/conformational transitions.

This paper is organized in the following way—firstly, we would discuss the tautomerisation process separately for each base pair and then we would present in details sweeps of the most important physico-chemical parameters along the IRC altogether for all investigated base pairs (Figures 1–12, Tables 1–8).

FIGURE 2

Figure 2. Geometric structures of the 11 key points describing the evolution of the I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·C*_O2(rWC) tautomerisation via the sequential SPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo. Coordinates of the 11 key points, their relative electronic energies ΔE (in kcal·mol⁻¹ obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum at T = 298.15) and imaginary frequencies ν_i (cm⁻¹) at the TSs of their interconversions are presented below them in brackets (see Table 3). For more detailed designations see Figure 1.

FIGURE 3

Figure 3. Profiles of: (A) the relative electronic energy ΔE, (B) the first derivative of the electronic energy with respect to the IRC (dE/dIRC), (C) the dipole moment μ, (D) the NBO charges q_NBO, (E) the distance R(H₁-H₉) between the H₁ and H₉ glycosidic hydrogens, (F) the α₁ (∠N1H₁(C)H₉(G)) and α₂ (∠N9H₉(G)H₁(C)) glycosidic angles, (G) the electron density ρ; (H) the Laplacian of the electron density Δρ, (I) the ellipticity ε at the (3,−1) BCPs, (J) the distance d_A···B between the electronegative A and B atoms; (K) the distance d_AH/HB between the hydrogen and electronegative A or B atoms and (L) the angle ∠AH···B of the covalent and hydrogen bonds along the IRC of the investigated I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·C*_O2(rWC) tautomerisation via the sequential SPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum.

FIGURE 4

Figure 4. Geometric structures of the 11 key points describing the evolution of the II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G*_N2·C(rWC) tautomerisation via the sequential SPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 4). For more detailed designations see Figure 2.

FIGURE 5

Figure 5. Profiles of physico-chemical parameters of the investigated II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G*_N2·C(rWC) tautomerisation via the sequential SPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum. For more detailed designations see Figure 3.

FIGURE 6

Figure 6. Geometric structures of the 9 key points describing the evolution of the III. G*·C*(rWC)↔G*′_N2·C(rWC) tautomerisation via the DPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 5). For more detailed designations see Figure 2.

FIGURE 7

Figure 7. Profiles of the physico-chemical parameters of the investigated III. G*·C*(rWC)↔G*′_N2·C(rWC) tautomerisation via the DPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum. For more detailed designations see Figure 3.

FIGURE 8

Figure 8. Geometric structures of the 9 key points describing the evolution of the IV. G*′·C*(H)↔G*_N7·C(H) tautomerisation via the DPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 6). For more detailed designations see Figure 2.

FIGURE 9

Figure 9. Profiles of the physico-chemical parameters of the investigated IV. G*′·C*(H)↔G*_N7·C(H) tautomerisation via the DPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum. For more detailed designations see Figure 3.

FIGURE 10

Figure 10. Geometric structures of the 9 key points describing the evolution of the V. G*′·C*(rH)↔G*′_N7·C(rH) tautomerisation via the DPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 7). For more detailed designations see Figure 2.

FIGURE 11

Figure 11. Profiles of the physico-chemical parameters of the investigated V. G*′·C*(rH)↔G*′_N7·C(rH) tautomerisation via the DPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum. For more detailed designations see Figure 3.

FIGURE 12

Figure 12. Profiles of the energy of the intermolecular H-bonds E_HB estimated by the EML formula at the (3,−1) BCPs along the IRC of the investigated tautomerisations via the SPT or DPT obtained at the B3LYP/6-311++G(d,p) level of theory (see Table 3).

TABLE 1

Table 1. Energetic (in kcal·mol⁻¹) and kinetic (in s) characteristics of the tautomerisation of the G*·C*(rWC), G*′·C*(H), and G*′·C*(rH) DNA base pairs via the SPT or DPT obtained at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of QM theory in the continuum with ε = 1 under normal conditions (see Figure 1).

TABLE 2

Table 2. Electron-topological, geometrical, and energetic characteristics of the intermolecular H-bonds in the investigated DNA base pairs in rare tautomeric forms and TSs of their tautomerization via the SPT or DPT obtained at the B3LYP/6-311++G(d,p) level of QM theory (ε = 1) (see Figure 1).

TABLE 3

Table 3. Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 11 key points and the polarity of the latters along the IRC of the I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·C*_O2(rWC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 2).

TABLE 4

Table 4. Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 11 key points and the polarity of the latters along the IRC of the II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G*_N2·C(rWC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 4).

TABLE 5

Table 5. Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latters along the IRC of the III. G*·C*(rWC)↔G*′_N2·C(rWC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 6).

TABLE 6

Table 6. Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latters along the IRC of the IV. G*′·C*(H)↔G*_N7·C(H) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 8).

TABLE 7

Table 7. Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latters along the IRC of the V. G*′·C*(rH)↔G*′_N7·C(rH) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 10).

TABLE 8

Table 8. Patterns of the specific intermolecular interactions including AH···B H-bonds and loosened A-H-B covalent bridges that sequentially replace each other along the IRC of the investigated tautomerisations via the SPT or DPT obtained at the B3LYP/6-311++G(d,p) level of theory (see Figure 12).

Tautomerisation of the Reverse Löwdin G*·C*(rWC) Base Pair via the SPT: I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·${\text{C}}_{\mathrm{\text{O2}}}^{*}$(rWC) and II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔${\text{G}}_{\mathrm{\text{N2}}}^{*}·$C(rWC)

For the first time we have discovered three local minima on the hypersurface of the electronic energy of the G*·C*(rWC) base pair corresponding to the high-energy tautomerised G·${\text{C}}_{\text{O}2}^{*}$(rWC), G⁺·C⁻(rWC), and ${\text{G}}_{\text{N}2}^{*}·$C(rWC) base pairs (Figure 1, Table 1). All of them are stabilized by the participation of three intermolecular H-bonds, among which the upper O6H…O2/O2H…O6 H-bonds are the strongest (Table 2).

In fact, the tautomerisation of the G*·C*(rWC) base pair with relative Gibbs free energy ΔG = 0.00 kcal·mol⁻¹ starts from the single transfer of the proton localized at the N3 nitrogen atom of the C base to the N1 nitrogen atom of the G base along the intermolecular H-bond (C)N3H…N1(G). This G*·C*(rWC)↔G⁺·C⁻(rWC) tautomerization process occurs via the TS_{G*·C*(rWC)↔G+·C⁻(rWC)} (C_s symmetry) (ΔG = 4.38 kcal·mol⁻¹) containing N1-H-N3 covalent bridge and further proceeds through the intermediate—tight ion pair G⁺·C⁻(rWC) (ΔG = 4.44 kcal·mol⁻¹) (C_s symmetry), which is the point of bifurcation. By the way, it should be noted that this is the first case of the reliable fixation of the ionic pair of bases, formed as a result of the SPT along the intermediate molecular H-bond, which is involved in its stabilization. Similar attempts to localize such structures for the A·T(WC) and G·C(WC) DNA base pairs didn't lead to result.

Further the G*·C*(rWC)↔G⁺·C⁻(rWC) tautomerisation reaction proceeds according two scenarios via the proton transfer along:

- the (G)O6H….O2(C) H-bond through the TS_{G⁺·C⁻(rWC)↔G·C*O2(rWC)} (ΔG = 3.64 kcal·mol⁻¹; C_s symmetry) with O6-H-O2 covalent bridge leading to the G·${\text{C}}_{\text{O}2}^{*}$(rWC) product (C_s symmetry);

- the (G)N2H….N4(C) H-bond through the TS_{G⁺·C⁻(rWC)↔G*N2·C(rWC)} (ΔG = 9.27 kcal·mol⁻¹; C_s symmetry) N2-H-N4 covalent bridge leading to the ${\text{G}}_{\text{N}2}^{*}$·C(rWC) product (C_s symmetry).

It attracts attention that electronic ΔE_int and Gibbs free ΔG_int energies of the interaction for the tautomerised G·${\text{C}}_{\text{O}2}^{*}$(rWC) (ΔE_int = −39.67/ΔG_int = −26.53) and ${\text{G}}_{\text{N}2}^{*}$·C(rWC) (ΔE_int = −41.10/ΔG_int = −26.10) base mispairs exceed the values for the initial G*·C*(rWC) base mispair (ΔE_int = −20.21/ΔG_int = −7.40) and also canonical G·C(WC) base pair (ΔE_int = −29.28/ΔG_int = −15.97 kcal·mol⁻¹) (Brovarets' and Hovorun, 2014a).

Moreover, it was revealed that all three formed high-energy complexes—the G⁺·C⁻(rWC) ion pair and G·${\text{C}}_{\text{O}2}^{*}$(rWC), ${\text{G}}_{\text{N}2}^{*}$·C(rWC) tautomers of the Löwdin G*·C*(rWC) base pair are dynamically unstable structures, since for them the zero energy of the vibrations, which frequency become imaginary at the TS of tautomerisation, significantly exceeds the reverse electronic barrier (363.8, 668.1, and 454.7 cm⁻¹) (Table 1). Moreover, Gibbs free energies of the reverse barrier for the G*·C*(rWC)↔G⁺·C⁻(rWC) and G⁺·C⁻(rWC)↔${\text{G}}_{\text{N}2}^{*}$·C(rWC) tautomeric transformations are negative (−0.06 and −1.12 kcal·mol⁻¹, accordingly) and for the G⁺·C⁻(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC)—it is less (0.13 kcal·mol⁻¹) than kT (0.62 kcal·mol⁻¹ under normal conditions) (Table 1).

So, in fact the Löwdin G*·C*(rWC) base pair does not tautomerise to the novel G·${\text{C}}_{\text{O}2}^{*}$(rWC) and ${\text{G}}_{\text{N}2}^{*}$·C(rWC) base mispairs via the SPT along the intermolecular H-bonds. However, despite this verdict, obtained data can be useful as an analogy or even as a heuristic push at the investigation of the tautomerisation mechanisms of the H-bonded complexes of any nature.

Tautomerisation of the Reverse Löwdin G*·C*(rWC) Base Pair via the DPT: III. G*·C*(rWC)↔G*′_N2·C(rWC)

We have also detected the unusual tautomerisation of the reverse Lowdin's G*·C*(rWC) DNA base mispair via the asynchronous [with a level of asynchrony 3.49 Bohr (Brovarets' and Hovorun, 2019b)] concerted DPT to the G*′_N2·C(rWC) DNA base mispair with trans-oriented N2H imino group of the G DNA base, in which participates the protons at the N3(C) and N2(G) nitrogen atoms moving in opposite directions. Unusual nature of this process consists in the fact that the transitions of the protons from N3(C) to N1(G) and from N2(G) to N4(C) along the intermolecular H-bonds provokes the rotation of the NH₂ amino group of the G base into the trans-position relatively the neighboring double C2N3(G) bond. As a results, this G*·C*(rWC)↔G*′_N2·C(rWC) tautomerisation reaction proceeds through the substantially non-planar intermediate – G^+′_N2·C⁻(rWC) ion pair with non-planar NH₂ amino group (C₁ symmetry), the substantially non-planar TS_{G*·C*(rWC)↔G*′N2·C(rWC)} (C₁ symmetry), and substantially non-planar product of this reaction—the G*′_N2·C(rWC) DNA base mispair (C₁ symmetry). This DNA base mispair is stabilized by the participation of the three intermolecular H-bonds—(G)O6H…O2(C), (G)N1H…N3(C), and (C)N4H…N2(G) and represents itself quite stable structure (ΔE_int = −33.41/ΔG_int = −18.99 kcal·mol⁻¹). Its characteristic structural feature is the substantial non-flatness (∠N1C6C2N3 = 23.3°; ∠C2N2N4C4 = 53.8°) and the exit from the plane of the purine ring of the O6H (∠HO6C6N1 = 10.8°), N1H (∠HN1C2N3 = -157.4°), and N2H (∠HN2C2N3 = -167.6°) external groups with the trans-orientation relative to the neighboring bond C2N3.

Moreover, we have revealed that the ${\text{G}}_{\text{N}2}^{*}·$C(rWC) and G*′_N2·C(rWC) DNA base pairs interconvert via the conformational rotation of the N2H imino group around the C2N2 bond through the Gibbs freee energy barrier 31.65 kcal·mol⁻¹ (Figure 1, Tables 1–2).

Tautomerisation of the Hoogsteen G*′·C*(H) Base Pair via the Classical DPT: IV. G*′·C*(H)↔${\text{G}}_{\mathrm{\text{N7}}}^{*}·$C(H)

The tautomerisation of the Hoogsteen G*′·C*(H) base pair (ΔG = 0.00 kcal·mol⁻¹; C_s symmetry) is possible via one-single way—through the asynchronous DPT (the values of the asynchronity consists 1.58 Bohr) (for more details see further discussion and Figure 8) along two intermolecular antiparallel lower (G)O6H…N4(C) and (C)N3H…N7(G) H-bonds through the TS_{G*′·C*(H)↔G*N7·C(H)} (ΔG = 4.01 kcal·mol⁻¹; C_s symmetry) connected by the N7-H-N3 covalent bridge with further formation of the dynamically-unstable ${\text{G}}_{\text{N}7}^{*}·$C(H) base mispair with small lifetime τ = 4.46·10⁻¹³ s (ΔG = 3.20 kcal·mol⁻¹; C_s symmetry). The G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}·$C(H) tautomerisation starts from the initial transfer of the hydrogen atom localized at the O6 oxygen atom of the G*′ DNA base to the N4 nitrogen atom of the C* DNA base within the G*′·C*(H) DNA base pair and then through the G⁺·C⁻(H) Hoogsteen base pair via the proton transfer from the N3 nitrogen atom to the N7 nitrogen atom leading to the formation of the ${\text{G}}_{\text{N}7}^{*}·$C(H) DNA base mispair by the participation of the rare ${\text{G}}_{\text{N}7}^{*}$ tautomer and canonical C DNA base.

Notably, that initial and final structures involved in this tautomerisation process are stabilized by the participation of three intermolecular H-bonds (Table 2), one of which (G)C8H…O2(C) is non-standard with energy 1.15 kcal·mol⁻¹.

Notably, electronic (ΔE_int = −35.66) and Gibbs free (ΔG_int = −22.05 kcal·mol⁻¹) energies of the interaction for the terminal ${\text{G}}_{\text{N}7}^{*}·$C(H) base mispair exceed the values for the initial base mispair (ΔE_int = −21.24/ΔG_int = −8.91 kcal·mol⁻¹). At this, total energies of the H-bonds make a great contribution to the electronic interaction energy−78.1% for the G*′·C*(H) DNA base mispair and 51.7% for the ${\text{G}}_{\text{N}7}^{*}·$C(H) DNA base mispair.

All low-frequency intermolecular vibrations of the ${\text{G}}_{\text{N}7}^{*}·$C(H) base mispair, which periods are in the range 8.06·10⁻¹³-1.16·10⁻¹² s, can't develop during its lifetime. This situation is typical for the structures, which are deprived of dynamic stability (Brovarets' and Hovorun, 2019b).

So, in this case in fact the G*′·C*(H) base pair does not tautomerise via the DPT similarly to the previous G*·C*(rWC) base pair.

Tautomerisation of the Reverse Hoogsteen G*′·C*(rH) Base Pair via the DPT by the Participation of the C8H(G*′) Group: V. G*′·C*(rH)↔G*^′_N7·C(rH)

The G*′·C*(rH) base pair differs from two previous ones, since it tautomerises via the asynchronous DPT (with the value of asynchronity 1.69 Bohr) along the intermolecular antiparallel (C)N3H…N7(G) and (G)C8H…N4(C) H-bonds with further formation of the yilidic form G*′_N7 of the G DNA base (Govorun et al., 1995a,b; Kondratyuk et al., 2000), which is characterized by the transferred proton of the C8H group to the neighboring N7 nitrogen atom. The G*′·C*(rH)↔G*′_N7·C(rH) tautomerisation proceeds via the initial transfer of the proton localized at the N3 nitrogen atom of C base to the N7 nitrogen atom of G base through the formation of the G^+′_N7·C⁻ ion pair followed by further proton transfer localized at the C8 carbon atom of G*′ base to the N4 nitrogen atom of C* base. Notably, that TS of this process—TS_{G*′·C*(rH)↔G*′N7·C(rH)}–has planar structure (C_s symmetry) and contains C8-H-N4 covalent bridge, which angle is 158.8°.

This process is become possible due to the fact that G base, from one side, is CH-acid (Kondratyuk et al., 2000) and from the other—it is able to transfer into the zwitterionic tautomer—so-called yilidic form (Govorun et al., 1995a,b; Kondratyuk et al., 2000). Analysis of the obtained data (Table 1) evidences that G*′_N7·C(rH) tautomer is dynamically stable structure with quite long lifetime (τ = 5.15·10⁻¹² s). Characteristically, that all 6 low-frequency intermolecular vibrations of the G*′_N7·C(rH) base mispair, which period are in the range 6.83·10⁻¹³-1.51·10⁻¹² s, can develop during this lifetime.

This is the first case (Brovarets' et al., 2018f), when the product of the tautomerization of the H-bonded base pair by the participation of the yilidic purine base is dynamically stable structure. However, formed G*′_N7·C(rH) base pair has low population−2.3·10⁻¹⁷ under normal conditions, which complicates the understanding of its biological role.

At the same time, such structures represent a considerable interest from a theoretical point of view, in particular, they contain unusual (C)N4H…C8⁻(G) H-bond (Table 2), which supplements existing data about the nature of the H-bonding in the pairs of DNA/RNA bases (Brovarets' et al., 2014e).

Profiles of the Physico-Chemical Parameters of the Investigated SPT and DPT Tautomerisations

We have investigated in details the mechanisms of the abovementioned processes of the tautomerisation of the reverse Lowdin's G*·C*(rWC), Hoogsteen G*′·C*(H), and reverse Hoogsteen G*′·C*(rH) base pairs via the PT along the intermolecular H-bonds. Tautomerisations proceed in a synchronous concerted manner via the stepwise SPT in the case of the I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) and II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔${\text{G}}_{\text{N}2}^{*}·$C(rWC) reactions, while in an asynchronous concerted manner via the DPT in the case of the III. G*·C*(rWC)↔G*′_N2·C(rWC), IV. G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H) and V. G*′·C*(rH)↔G*′_N7·C(rH) reactions (Figures 2, 4, 6, 8, 10, Tables 3–7).

We have established following regularities of the general character for the obtained sweeps of the most important physico-chemical parameters along the IRC.

The widths of the reaction zone of the investigated reactions starting from the reagent and till the product are almost the same for the I. G*·C*(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) (9.24); II. G*·C*(rWC)↔${\text{G}}_{\text{N}2}^{*}$·C(rWC) (10.54) and IV. G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H) (9.30 Bohr), while these widths are significantly larger for the III. G*·C*(rWC)↔G*′_N2·C(rWC) (14.49) and V. G*′·C*(rH)↔G*′_N7·C(rH) (23.12 Bohr) reactions (Figures 2, 4, 6, 8, 10).

All tautomerisation processes are dipole-active, since they are followed by the significant change of the dipole moment μ of the tautomerising base pair (Figures 3C, 5C, 7C, 9C, 11C). These dependencies are U-like with maximal and minimal values located in the transition state zone for the I. G*·C*(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) SPT (values of μ change in the range: 3.15–6.54); II. G*·C*(rWC)↔${\text{G}}_{\text{N}2}^{*}$·C(rWC) SPT (3.15–7.15); III. G*·C*(rWC)↔G*′_N2·C(rWC) DPT (2.81–8.84) and V. G*′·C*(rH)↔G*′_N7·C(rH) DPT (4.47–9.01 D) reactions, while it is reverse with maximal values at the transition state zone for the IV. G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H) reaction (5.16–10.12 D) DPT (Figures 3C, 5C, 7C, 9C, 11C).

Tautomerisation process does not change the configuration of the base pair—complexes slightly compress on several dozens of Angstrom at the zone of the TSs of tautomerisation. TSs demonstrate significant deviations from a plane in the case, when steric conflicts arise between the interacting exocyclic groups (Figures 2, 4, 6, 8, 10).

According to the authors' conception (Brovarets' and Hovorun, 2013a,b,c,d, 2014c,d, 2015h,i; Brovarets' et al., 2013a,b, 2014a,b,c, 2015), it was introduced key points, namely 11 key points were obtained in the cases of the I. G*·C*(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) and II. G*·C*(rWC)↔${\text{G}}_{\text{N}2}^{*}$·C(rWC) SPT along the IRC in contrast to the processes of the III. G*·C*(rWC)↔G*′_N2·C(rWC), IV. G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H) and V. G*′·C*(rH)↔G*′_N7·C(rH) DPT, for which 9 key points have been localized.

At this, it was obtained typical crossings of the profiles for the electron density ρ, the Laplacian of the electron density Δρ and the distance d_AH/HB between the hydrogen and electronegative A or B atoms for the H-bonds involved in the tautomerisation, notifying the equalization of these parameters. They occur at the 3rd and 9th key points in the case of the reaction I, 3rd and 8th—for the reaction II, 3rd and 7th—for the reactions III and IV and 3rd and 6th—for the reaction V (Figures 3G,H,K, 5G,H,K, 7G,H,K, 9G,H,K, 11G,H,K).

One and the same regularity is observed for the dE/dIRC function in all cases of tautomerisations—with two local maxima and two local minima achieved at the TS zone (Figures 3B, 5B, 7B, 9B, 11B).

Also it was observed five patterns for the energy E_HB of the intermolecular H-bonds, estimated by the EML method (Espinosa et al., 1998; Matta et al., 2006b; Mata et al., 2011; Lecomte et al., 2015; Alkorta et al., 2016, 2017), along the IRC for the I, II, IV and V reactions and four patterns—for the III reaction (Figure 12, Table 8). These sweeps allow to estimate numerically the cooperativity of the neighboring H-bonds according to the methodology, proposed by us earlier (Brovarets' and Hovorun, 2019b). It was established the general pattern—the anti-parallel H-bonds amplify each other and parallel—weaken each other (Turaeva and Brown-Kennerly, 2015). Moreover, some of the dependencies of the energy E_HB of the intermolecular H-bonds exist during entire IRC, such as (G)N2H…N4(C) for the I. G*·C*(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) reaction, (G)O6H…O2(C) for the II. G*·C*(rWC)↔${\text{G}}_{\text{N}2}^{*}$·C(rWC) reaction, (G)O6H…O2(C) for the III. G*·C*(rWC)↔G*′_N2·C(rw_WC) reaction, (G)C8H…O2(C) (its energy remains almost unchangeable during the IRC) for the G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H) reaction and (G)O6H…O2(C) for the G*′·C*(rH)↔G*′_N7·C(rH) reaction. In the case of the III. G*·C*(rWC)↔G*′_N2·C(rw_WC) reaction, some of the H-bonds transform into the van der Waals contact and then to another H-bonds during the IRC: (G)N2H…N4(C) H-bond → (G)N2…N4(C) vdW contact → (G)N2H…N4(C) H-bond for the III. G*·C*(rWC)↔G*′_N2·C(rw_WC) reaction (Figure 12). For more details according the patterns refer to Table 8.

Finally, we would like to note some general regularities, which are characteristic for all without exclusion processes of tautomerisation.

Thus, in the vast majority of cases base pairs are plane symmetric structures during the entire PT and DPT tautomerization processes along the IRC, despite the ability of the DNA bases for the out-of-plane bending (Govorun et al., 1992; Hovorun et al., 1999; Nikolaienko et al., 2011), excluding two mentioned above cases, when there are deviation from the planarity—III. G*·C*(rWC)↔G*′_N2·C(rWC) (Figure 1).

Interestingly, the total energy of the intermolecular H-bonds only partially contributes to the electron energy of the monomers interactions among all without any exceptions H-bonded structures investigated in this work (see Figures 1, 12). This result is in a good accordance with generalized literature data (Brovarets' and Hovorun, 2014e, 2019b).

Conclusions

For the first time the tautomerisation of the biologically-important conformers of the G*·C* DNA base pair - reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H) and reverse Hoogsteen G*′·C*(rH) pairs - was investigated and thoroughly analyzed. It was found out that the G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) and G*·C*(rWC)↔G⁺·C⁻(rWC)↔${\text{G}}_{\text{N}2}^{*}·$C(rWC) tautomerization processes occur via the two-stage sequential SPT via dynamically-unstable zwitterion-like G⁺·C⁻(rWC) intermediate, while the G*·C*(rWC)↔G*′_N2·C(rw_WC), G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}$·C(H), and G*′·C*(rH)↔G*′_N7·C(rH) tautomerization processes occur through the one-stage DPT. At this, proton transfer along the non-canonical (G*)CH…N(C*) H-bond is accompanied by the significant deviation of the C-H-N bridge at the TS.

Obtained data evidence that among the G*·C*(rWC), G′·C*(H) and G*′·C*(rH) base pairs only the tautomerisation of the latest of them lead to the formation of the dynamically stable G*′_N7·C(rH) base pair with lifetime 5.15 ps with a miserable population 2.3·10⁻¹⁷.

Moreover, it was revealed that the I. G*·C*(rWC)↔G⁺·C⁻(rWC)↔G·${\text{C}}_{\text{O}2}^{*}$(rWC) and II. G*·C*(rWC)↔G⁺·C⁻(rWC)↔${\text{G}}_{\text{N}2}^{*}·$C(rWC) tautomerization reactions proceed in a synchronous concerted manner via the stepwise SPT, while the III. G*·C*(rWC)↔G*′_N2·C(rWC), IV. G*′·C*(H)↔${\text{G}}_{\text{N}7}^{*}·$C(H), and V. G*′·C*(rH)↔G*′_N7·C(rH) reactions occur in an asynchronous concerted manner via the DPT.

We have also established dependencies of the most important physico-chemical parameters along the IRC enabling to understand more precisely the inherent nature of the investigated processes.

Data Availability

The datasets generated for this study are available on request to the corresponding author.

Author Contributions

OB analysis and preparation of the current literature survey, discussion of the strategy of the current investigation, study conception and design, acquisition of data, drafting of manuscript analysis and interpretation of data, performance of calculations, discussion of the obtained data, preparation of the numerical data for Tables 1–8, graphical materials for Figures 1–12, and text of the manuscript. TO preparation of the numerical data for Tables 1–8 and graphical materials for Figures 1–12. DH study conception, critical revision of manuscript, proposition of the task of the investigation, discussion of the obtained data, and preparation of the text of the manuscript. All authors were involved in the proofreading of the final version of the manuscript.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

Authors sincerely grateful for technical support to Dr. Ivan Voiteshenko (Taras Shevchenko National University of Kyiv) and computational facilities of joint computer cluster of SSI Institute for Single Crystals of the National Academy of Sciences of Ukraine (NASU) and Institute for Scintillation Materials of the NASU incorporated into Ukrainian National Grid. DrSci OB expresses sincere gratitude to the U.S.-Ukraine Foundation (USUF) Biotech Initiative for a travel grant (2018 Emerging Biotech Leader of Ukraine; https://www.usukraine.org/biotechnology-initiative/), enabling to participate in the 63rd Annual Meeting of the Biophysical Society BPS'2019 (Baltimore, Maryland, March 2–6, 2019; https://www.biophysics.org/2019meeting#/; https://bioukraine.org/news/emerging-biotech-leader-olha-brovarets-attends-63rd-biophysical-society-meeting-in-baltimore/; https://bioukraine.org/news/emerging-leader-olha-brovarets-shares-her-us-experience-with-bionity-student-biotech-club/).

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