Non-dissociative structural transitions of the Watson-Crick and reverse Watson-Crick А·Т DNA base pairs into the Hoogsteen and reverse Hoogsteen forms

In this study it was theoretically shown that discovered by us recently (Brovarets’ et al., Frontiers in Chemistry, 2018, 6:8; doi: 10.3389/fchem.2018.00008) high-energetical, significantly non-planar (symmetry C1), short-lived wobbled conformers of the classical Watson-Crick А·Т(WC), reverse Watson-Crick А·Т(rWC), Hoogsteen А·Т(Н) and reverse Hoogsteen А·Т(rН) DNA base pairs are the intermediates of their pairwise А∙Т(WC)/А∙Т(rWC) ↔ А∙Т(H)/А∙Т(rH) conformational transformations. These transitions do not require for their realization the energy-consumable anisotropic rotation of the amino group of A around the exocyclic C6-N6 bond. They are controlled by the non-planar transition states with quasi-orthogonal geometry (symmetry C1) joined by the single intermolecular (Т)N3H···N6(А) H-bond (~4 kcal∙mol−1). The Gibbs free energies of activation for these non-dissociative, dipole-active conformational transitions consist 7.33 and 7.81 kcal∙mol−1, accordingly. Quantum-mechanical (QM) calculations in combination with Bader’s quantum theory of “Atoms in Molecules” (QTAIM) have been performed at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of QM theory in the continuum with ε = 4 under normal conditions.

In this case conformational transformations are controlled by the soft, non-planar TSs, stabilized by the participation of the single intermolecular (Т)N3H···N6(А) H-bond between the imino group of T and pyramidilized amino group of A. The Gibbs free energies of activation for these non-dissociative, dipole-active conformational transitions consist 7.33 and 7.81 kcal•mol −1 , accordingly.

Computational Methods
We have calculated geometries of the basic and high-energetic conformers and transition states (TSs) of their mutual conformational transformations together with their harmonic vibrational frequencies at the B3LYP/6-311++G(d,p) level of theory [36][37][38][39][40] , using Gaussian'09 package 41 , in the continuum with ε = 4, which is typical for the processes in real biological complexes and taking into account the structural and functional characteristics of the bases in the duplex DNA and at the same time satisfactorily reflecting the environment in the essentially hydrophobic base-pair recognition pocket of the high-fidelity DNA-polymerase  . Considered level of theory has been successfully applied for the calculations of the similar tasks and systems [47][48][49][50][51][52][53][54][55] . A scaling factor of 0.9668 [55][56][57][58][59][60][61] has been used in order to correct the harmonic frequencies of all bps and TSs of the transitions between them. The local minima or TSs, localized by Synchronous Transit-guided Quasi-Newton method 62 , have been appointed to the complexes on the potential energy landscape containing any or one imaginary frequency in their vibrational spectra, accordingly. We used TS theory in order to estimate the activation barriers of the conformational transformations 63 . Electronic energy calculations have been performed at the single point at the MP2/aug-cc-pVDZ level of theory 67,68 .
The Gibbs free energy G for all structures has been received at the MP2/6-311++G(2df,pd) level of theory by the formula: el corr where E el -electronic energy, while E corr -thermal correction. The electronic energies of interaction ∆E int have been obtained at the MP2/6-311++G(2df,pd) level of theory as a difference between the BSSE-corrected 69-72 electronic energy of the bp and electronic energies of the isolated bases.
The energies of the attractive van der Waals contacts 85,86 in TSs of the conformational transitions have been estimated by the Espinosa-Molins-Lecomte (EML) formula 87,88 : where V(r) -value of a local potential energy at the (3, −1) BCP. The energies of the conventional AH···B H-bonds have been calculated by the Iogansen's formula 89 : where Δν -frequency shift of the stretching mode of the H-bonded AH group involved in the AH···B H-bond relatively the unbound group. We applied the partial deuteration in order to avoid the effect of vibrational resonances 90,91 .
In this study the numeration for the DNA bases is generally accepted 92 .
In this study we have provided investigations at the basic, but sufficient level of the isolated H-bonded pairs of nucleotide bases, that adequately simulates the processes in real biological systems [93][94][95] , in particular in the base-pair recognition pocket of the high-fidelity DNA-polymerase [42][43][44][45][46] . At this, we have relied on the experience received in the previous works 11,96-98 on the related topic and systems, in which the negligibly small impact of the stacking and sugar-phosphate backbone on the tautomerisation processes has been shown.

Results and Their Discussion
In our previous paper 11  High-energetic mechanism of the WC/rWC ↔ H/rH conformational transitions of the А•Т DNA bps is connected with anisotropic rotation of the amino group of A around the exocylic С6-N6 bond 35 Table 2); carbon atoms are in light-blue, nitrogen -in dark-blue, hydrogenin grey and oxygen -in red. Exclusively enantiomers of one type are presented.  Table 1. Energetic characteristics (in kcal•mol −1 ) of the discovered conformational transitions of the four biologically important А·Т DNA bps obtained at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 4 (see Fig. 1). a Imaginary frequency at the TS of the conformational transition, cm  Table 3. Selected geometrical parameters, characterizing the non-planarity of the discovered conformers with wobble geometry of the four biologically important А·Т DNA bps and TSs of their conformational interconversions, obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 4. Note: Signs of the dihedral angles are presented exclusively for one type of enantiomers.  Table 2. Electron-topological, geometrical and energetic characteristics of the intermolecular specific contacts in the investigated conformers of the А·Т DNA bps and TSs of their conformational transformations obtained at the B3LYP/6-311++G(d,p) level of theory (ε = 4) (see Fig. 1). a The electron density at the (3, −1) BCP of the specific contact, a.u. b The Laplacian of the electron density at the ( Of course, in the composition of DNA these conformational transitions represent a self-consistent transformation of the bps, the anti ↔ syn transition of A around the glycosidic bond (ΔΔG TS = 3.4 kcal•mol −1 at χ TS = 121 • for BI-conformer of the isolated 2′-deoxyadenosine 102 ) and reorganization of stacking and hydratation 8 . Simple comparison of the energetics, determining these processes, clearly indicates that the first two of them plays a leading role. This fact gives hope that obtained in this paper data are closely related to the nature of the А•Т(WC) ↔ А•Т(H) thermal fluctuation process, which occurs in DNA [1][2][3][4][5][6][7] . This conclusion can be verified, applying the newest methods of ab initio dynamics for the short fragments of DNA.

Conclusions
By applying developed by us novel ideas according the high-energetic conformers of the classical А•Т DNA bps 11 , we offered novel non-dissociative mechanisms of the А•Т(WC) ↔ А•Т(H) and А•Т(rWC) ↔ А•Т(rH) conformational transitions, that do not require for their realization energy-consuming anisotropic rotation of the amino group of the A DNA base around the C6-N6 exocyclic bond. Figuratively speaking, at the transformation of the A base from the anti-to syn-conformation leading to the formation of the Hoogsteen А•Т(H) and reverse Hoogsteen А•Т(rH) bps, it dynamically relies as on the support on the T DNA base through the pyramidilized amino group of A, interacting with it in the TS region by one single (Т)N3H···N6(А) H-bond.
In the light of the obtained by us results, it could be suggested that the А•Т(WC) ↔ А•Т(H) conformational transition in DNA duplex, which was registered experimentally 1-7 , most likely occurs by the non-dissociative mechanism: A, rotating from the anti-to syn-configuration, interacts with T via the intermolecular H-bonds along the entire process of the conformational transformation.