Atomistic mechanisms of the tautomerization of the G·C base pairs through the proton transfer: quantum-chemical survey

This study is devoted to the investigation of the G·C*tO2(WC)↔G*NH3·C*t(WC), G·C*O2(WC)↔G*NH3·C*(WC) and G*·C*O2(WC)↔G*NH3·C(wWC)↓ tautomerization reactions occurring through the proton transfer, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory in gas phase under normal conditions (‘WC’ means base pair in Watson-Crick configuration, T=298.15 K). These reactions lead to the formation of the G*NH3·C*t(WC), G*NH3·C*(WC) and G*NH3·C(wWC)↓ base pairs by the participation of the G*NH3 base with NH3 group. Gibbs free energies of activation for these reactions are 6.43, 11.00 and 1.63 kcal·mol-1, respectively. All of these tautomerization reactions are dipole active. Finally, we believe that these non-dissociative processes, which are tightly connected with the tautomeric transformations of the G·C base pairs, play an outstanding role in supporting of the spatial structure of the DNA and RNA molecules with various functional purposes.


Introduction
In recent years according to the analysis of the literature [1][2][3][4][5][6][7], the interest of researchers to the investigation of the prototropic tautomerism significantly increased. It is obviously connected with the fact that this research topic is multidisciplinary and covers wide areas of knowledge such as chemistry, biochemistry, structural and quantum biology, molecular and quantum pharmacology, condensed matter physics, crystal physics, electronic technologies, and biomolecular technologies [8][9][10][11][12][13].
It occurs as intensive accumulation of the data within the framework of the classical models, describing these processes [14][15][16][17][18], as well as successful searches of both novel atomistic mechanisms of the prototropic tautomerization of the molecular objects [19][20][21][22] and novel instruments for the penetration into the course of these processes.
Shortly saying, now the mechanisms of the tautomerization of the base pairs, which are accompanied by significant changing of their geometry [23][24][25][26], actively enter the arena. It is suggested that exactly these tautomeric transitions are not only responsible for the structural transitions in the nucleic acids, but also for the supporting of their unique spatial structures, having certain biological functions.
Aim of this work is to deepen the existing ideas about the quantum mechanisms of the tautomerization of the G·C pairs of nucleotide bases through the proton transfer along the intermolecular neighboring H-bonds as their intrinsic property. We have chosen for its successful realization biologically important G·C base pairs, which monomers are in the basic and rare tautomeric forms.
As a result of the provided quantum-chemical investigations for the first time the following regularities were revealed.
Tautomerizations of the G·C base pairs are controlled by the transition states, joined by the intermolecular H-bonds and covalent bridges.
In all cases without any exception, mechanisms of the tautomerization are step-by-step realized by the proton transfer.

Density functional theory calculations of the geometry and vibrational frequencies
Equilibrium geometries of the investigated G·C base pairs and transition states (TSs) of their tautomerizations and rotations, as well as their harmonic vibrational frequencies have been calculated using Gaussian'09 program package [27] at the B3LYP/6-311++G(d,p) level of theory [28][29][30][31][32], which approved itself successfully for the calculations of the similar systems and processes, and shown acceptable level of accuracy and adequacy of the obtained results [32,33]. A scaling factor that is equal to 0.9668 has been applied in the present work for the correction of the frequencies for all complexes [21,22,34].
We have confirmed local minima and transition states, localized by Synchronous Transit-guided Quasi-Newton method [35], on the potential energy landscape by the absence or presence, respectively, of one imaginary frequency in the vibrational spectra of the complexes.
All reaction pathways have been reliably confirmed by providing intrinsic reaction coordinate (IRC) calculations [35] from each TS in the forward and reverse directions at the B3LYP/6-311++G(d,p) level of theory.
All calculations have been performed in the continuum with ε=1 that adequately reflects the processes occurring in real biological systems without deprivation of the structurally functional properties of the bases in the composition of the DNA or RNA molecules and satisfactorily models the substantially hydrophobic recognition pocket of the DNA-polymerase machinery as a part of the replisome [36,37].

Single point energy calculations
We continued geometry optimizations with electronic energy calculations as single point calculations at the MP2/6-311++G(2df,pd) level of theory [38,39].
The Gibbs free energy G for all structures was obtained in the following way: where E el is the electronic energy and E corr -the thermal correction. (1)

QTAIM analysis
Bader's quantum theory of atoms in molecules (QTAIM) [40] was applied to analyze the electron density distribution, using program package AIMAll [41].
The presence of the bond critical point (BCP), namely, the so-called (3,-1) BCP, and a bond path between donor and acceptor of the H-bond or van der Waals contact, as well as the positive value of the Laplacian at this BCP (Δρ>0), were considered as criteria for the formation of the H-bond or van der Waals contact, respectively [42][43][44][45]. Wave functions were obtained at the B3LYP/6-311++G(d,p) level of theory, used for geometry optimization.
The atomic numbering scheme for the bases is conventional and rare tautomeric forms of the G and C bases are marked by an asterisk (*) [4].

Obtained results and their discussion
In this work investigated tautomerization pathways of the G·C base pairs are presented on Figure 1, and their discussion is outlined below.
It is interesting to note that G·C* t O2 (WC) base pair tautomerizes (Fig. 1a) through the double proton transfer along the N1H…N3 and O2H…N2 H-bonds and via the TS G·C*tO2(WC)↔G*NH3·C*t(WC) , which is stabilized by the participation of the two intermolecular (C)N4H…O6(G) and (C)O2H…N2(G) H-bonds, and (G)N1-H-N3(C) covalent bridge. Eventually, this reaction leads to the formation of the G* NH3 ·C* t (WC) base pair, stabilized by three intermolecular N4H…O6, N3H…N1, and N2H…O2 H-bonds. Exactly the proton transfer along the lower O2H…N2 H-bond leads to the formation of the NH 3 group at the G base.
Another G·C* O2 (WC)↔G* NH3 ·C*(WC) tautomerization reaction (Fig. 1c) occurs via the transfer of the proton, localized at the N1 nitrogen atom of the G base, to the N3 nitrogen atom of the C* O2 base and of the proton, localized at the O2 oxygen atom of the C* O2 base, to the N2 atom of the NH 2 amino group of the G base and finally leads to the G* NH3 ·C*(WC) base pair by the participation of the G* NH3 base with NH 3  Formed G* NH3 ·C*(WC) base pair can transform (Fig. 1d) by the mutual rotation of the bases around the middle N3H…N1 H-bond into the reverse G·C(rw WC ) base pair. Transition state TS G*NH3·C*(WC)↔G·C(rwWC) of this reaction is joined by three intermolecular N3H…N1, N2H…N4, and N2H…O2 H-bonds, and N2…N3 van der Waals contact. Finally, this G* NH3 ·C*(WC)↔G·C(rw WC ) reaction leads to the G·C(rw WC ) base pair.
The most interesting case represents the G*·C* O2 (WC )↔G* NH3 ·C(w WC ) ↓ transformation (Fig. 1e), since proton transfer within the G*·C* O2 (WC) base pair leads not only to the changing of its tautomeric status, but also to its geometrical rearrangement. G*·C* O2 (WC) base pair tautomerizes through the proton transfer along the upper O6H…N4 and lower O2H…N2 H-bonds from the O6 atom of the G* base to the N4 atom of the C* O2 base and from the O2 atom of the C* O2 base to the N2 atom of the G* base, respectively, via the TS G*·C*O2(WC)↔G*NH3·C(wWC)↓ . Finally, C base shifts down accordingly the G* NH3 base, forming the G* NH3 ·C(w WC ) ↓ base pair by the participation of the G* NH3 base with NH 3 group.
Considered G·C base pairs form the following order in terms of their relative Gibbs free ΔG and electronic ΔE energies (in kcal·mol -1 ): G·C(rw WC ) (0.00 and 0.00) < G* NH3 ·C(w WC ) ↓ (16.
In all cases without any exception tautomeric transitions are dipole active (μ=6.91-11.51 D) with minimum realized at the starting G·C* t O2 (WC) (9.98 D), G·C* O2 (WC) (7.91 D), and G*·C* O2 (WC) (6.91 D) base pairs. Authors' contributions OB-idea formulation, setting of the task, calculation of the data, building of the graphs, data extrapolation, preparing, and proofreading of the draft of the manuscript. AM-idea formulation, calculation of the data, preparing, and proofreading of the draft of the manuscript. DH-idea formulation, preparing, and proofreading of the draft of the manuscript. All authors contributed to the article and approved the submitted version.

Availability of data and material Not applicable.
Code availability Gaussian'09 program package -gaussian.com; AIM-