The A·T(rWC)/A·T(H)/A·T(rH) ↔ A·T*(rwWC)/A·T*(wH)/A·T*(rwH) mutagenic tautomerization via sequential proton transfer: a QM/QTAIM study

In this study for the first time we have revealed by QM and QTAIM calculations at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of QM theory the novel routes of the mutagenic tautomerization of three biologically important A·T DNA base pairs – reverse Watson–Crick A·T(rWC), Hoogsteen A·T(H) and reverse Hoogsteen A·T(rH) – followed by their rebuilding into the wobble (w) A·T*(rwWC), A·T*(wH) and A·T*(rwH) base mispairs by the participation of the mutagenic tautomers of the DNA bases (denoted by asterisk) and vice versa, thus complementing the physico-chemical property of the canonical A·T(WC) Watson–Crick DNA base pair reported earlier (Brovarets' et al., RSC Adv., 2015, 5, 99594–99605). These non-dissociative tautomeric transformations in the classical A·T(rWC), A·T(H) and A·T(rH) DNA base pairs proceed similarly to the canonical A·T(WC) DNA base pair via the intrapair sequential proton transfer with shifting towards major or minor grooves of DNA followed by further double proton transfer along the intermolecular H-bonds and are controlled by the plane symmetric and highly stable transition states – tight ion pairs formed by the A+ nucleobase, protonated by the N1/N7 nitrogen atoms, and T− nucleobase, deprotonated by the N3H imino group. Comparison of the estimated populations of the tautomerised states (10−21 to 10−14) with similar characteristics for the canonical A·T(WC) DNA base pair (10−8 to 10−7) leads authors to the conclusion, that only a base pair with WC architecture can be a building block of the DNA macromolecule as a genetic material, which is able for the evolutionary self-development. Among all four classical DNA base pairs, only A·T(WC) DNA base pair can ensure the proper rate of the spontaneous point errors of replication in DNA.


Introduction
Clarication of the microstructural mechanisms of the mutagenic tautomerization of the DNA base pairs is a classical problem of molecular biophysics, biochemistry and structural biology, which remain topical up to now. [1][2][3][4][5] Literature analysis shows that the so-called tautomeric hypothesis formulated by Watson and Crick, 1 soon aer their discovery of the spatial architecture of DNAa macromolecule that is the carrier of the genetic information, 2 represents itself the most vivid theoretical platform for the conduction of these studies. At that time, this hypothesis became a real breakthrough in the understanding of the nature of the origin of the spontaneous point mutationstransitions and transversions 5and also involvement in this biologically important phenomenon of the prototropic tautomerism of the DNA bases. 6,7 Advances in technology eventually led to numerous as experimental investigations, [8][9][10][11][12][13] in particular X-ray analysis 8,9 and NMR, in particular relaxation dispersion, measurements, 10-13 so theoretical examinations [14][15][16][17][18][19] of this discovery. However, these results do not clarify the physico-chemical mechanisms of the arising of the rare or mutagenic tautomeric forms of the DNA bases 20-23 (here and below marked by an asterisk).
Thus, in particular, it was found out that the A$T(WC) Watson-Crick DNA base pair exists simultaneously in three other biologically important hypostasis 45short-lived wobble A*$T(w) (population ¼ 5.4 Â 10 À8 ), A$T * O2 ðwÞ (9.9 Â 10 À9 ) and A$T*(w) (2.5 Â 10 À10 ) H-bonded mismatches, containing mutagenic tautomers of the nucleotide bases. Their forced separation by the DNA-polymerase machinery into the monomers with necessity generates mutagenic tautomers of the DNA bases, which are long-lived structures causing spontaneous point mutationstransitions and transversions. [53][54][55] Presented approach claries the microstructural mechanisms of the mutations induced by the classical mutagens, in particular 2-aminopurine, for which frequencies agree well with the experimental data. [56][57][58][59][60][61] The aim of the current study is to extend the approach launched in our previous work for the canonical DNA base pairs 45 to the other classical A$T DNA base pairsreverse Watson-Crick A$T(rWC), Hoogsteen A$T(H) and reverse Hoogsteen A$T(rH).
At this point, the question arises according the urgency of this investigation.
First, the A$T(rWC), A$T(H) and A$T(rH) DNA base pairs have a remarkable biological meaning (see works [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79] and the bibliography cited therein). Second, as of today, the mutagenic tautomerization of these biologically important pairs has not even mentioned in the literature. Thirdly, we are interested in the investigation of the evolutionary aspect of the problem, in particular, why Nature chose precisely Watson-Crick DNA base pairs for the construction of the genetic material, among which the A$T(WC) DNA base pair is the most evolutionarily distant, since it was the rst to appear evolutionary. 6,80,81 So, in this regard, we can make an assumption that exactly the A$T(WC) base pair provides necessary frequency of the spontaneous point replication errors in DNA, which lies in the range of 10 À9 to 10 À11 per nucleotide, incorporated during one replication cycle. 82,83 Such statement of the problem except merely academic value has also practical assignment, e.g. for the biomolecular electronics, which are used for the DNA-based carriers of the digital information, 84,85 since it allows, in principle, to understand how the complementary bases should be modied in order to suppress the tautomeric instability of their pair. This is extremely important for increasing of the accuracy of such molecular devices. 86 As a result of the systematic quantum-mechanical calculations, we managed to establish the microstructural mechanisms of the mutagenic tautomerisation of the studied A$T DNA base pairs and to reach the conclusion about a unique place of the canonical Watson-Crick A$T(WC) DNA base pair among them. Only this base pair able to provide the necessary rate of the spontaneous point mutations, which, as it is well known, are the source of the genome self-development. 6,[80][81][82][83] Computational methods Geometries of the investigated DNA base pairs and transition states (TSs) of their mutual tautomeric transformations, as well as their harmonic vibrational frequencies have been calculated at the B3LYP/6-311++G(d,p) level of theory, 87-91 using Gaussian'09 package 92 followed by the IRC calculations in the forward and reverse directions from each TS using Hessianbased predictor-corrector integration algorithm. 93 Applied level of theory has proved itself successful for the calculations of the similar systems. 94-96 A scaling factor that is equal to 0.9668 (ref. [97][98][99][100] has been applied in the present work for the correction of the harmonic frequencies for all DNA base pairs and TSs of their tautomeric transitions. We have conrmed the local minima and TSs, localized by Synchronous Transit-guided Quasi-Newton method, 101 on the potential energy landscape by the absence or presence, respectively, of the imaginary frequency in the vibrational spectra of the complexes. We applied standard TS theory for the estimation of the activation barriers of the tautomeric transformations. 102 Electronic energy calculations have been performed at the MP2/aug-cc-pVDZ level of theory. 103,104 The Gibbs free energy G for all structures was obtained in the following way: where E elelectronic energy, while E corrthermal correction. The time s 99.9% necessary to reach 99.9% of the equilibrium concentration of the reactant and product in the system of reversible rst-order forward (k f ) and reverse (k r ) reactions can be estimated by the formula: 102 The lifetime s of the formed mismatches has been 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 obtained as: 102 where quantum tunneling effect has been accounted by Wigner's tunneling correction, 105 which has been successfully used for the DPT reactions: 33-42  Table 2); carbon atoms are in light-blue, nitrogenin dark-blue, hydrogenin grey and oxygenin red.
This journal is © The Royal Society of Chemistry 2018 where k B -Boltzmann's constant, h -Planck's constant, DDG f,r -Gibbs free energy of activation for the tautomerisation reaction in the forward (f) and reverse (r) directions, n imagnitude of the imaginary frequency associated with the vibrational mode at the TSs.
Electronic interaction energies DE int have been calculated at the MP2/6-311++G(2df,pd) level of theory as the difference between the total energy of the base pair and energies of the monomers and corrected for the basis set superposition error (BSSE) 106,107 through the counterpoise procedure. 108,109 Bader's quantum theory of atoms in molecules (QTAIM), 110-115 using program package AIMAll, 116 was applied to analyse the electron density distribution. The presence of the bond critical point (BCP), namely the so-called (3,À1) BCP, and a bond path between hydrogen donor and acceptor, as well as the positive value of the Laplacian at this BCP (Dr > 0), were considered as criteria for the H-bond formation. 117,118 Wave functions were obtained at the level of theory used for geometry optimisation. The energies of the AH/B conventional H-bonds were evaluated by the empirical Iogansen's formula: 119 where Dnmagnitude of the frequency shi of the stretching mode of the H-bonded AH group involved into the AH/B Hbond relatively the unbound group. The partial deuteration was applied to minimize the effect of vibrational resonances. [120][121][122] The energies of the weak CH/O/N H-bonds 123,124 were calculated by the empirical Espinosa-Molins-Lecomte formula 125,126 based on the electron density distribution at the (3,À1) BCPs of the H-bonds: where V(r)value of a local potential energy at the (3,À1) BCP.
where rthe electron density at the (3,À1) BCP of the H-bond. The atomic numbering scheme for the DNA bases is conventional. 128

Results and their discussion
In this work based on the results obtained in the pioneering publication, 45 devoted to the novel WC 4 w mutagenic tautomerization of the canonical A$T(WC) and G$C(WC) DNA base pairs, we have investigated for the rst time the microstructural mechanisms of the mutagenic tautomerisation of the three other biologically important A$T DNA base pairs 62-79 -
It was found that the mutagenic tautomerization of each of these classical base pairs is controlled by the two TSs, representing itself tight (electronic energy of the bases interaction $120-129 kcal mol À1 ) ion pairs (A + nucleobase, protonated by the N1/N7 nitrogen atoms)$(T À nucleobase, deprotonated by the N3H imino group) with plane symmetric (C s symmetry) quasi-wobble structure. The term "quasi-wobble" means that these structures are no longer rWC/H/rH, but are not yet wobble. Notably, they differ from each other by the shiing direction of the T À respectively A + (towards major or minor groove of DNA) and also by the number of the H-bonds, which participate in their stabilization,three or four,one or two of them are characterized by the increased ellipticity (Fig. 1, Table 2). The latter points to the dynamic instability of these H-bonds. 31,97 Thus, the TS A þ $T À A$TðrWCÞ4A$T*O2ðrwWCÞ ;  Table 2). Table 1 Energetic (in kcal mol À1 ) and kinetic (in s) characteristics of the tautomerization of the classical A$T DNA base pairs into the wobble base mispairs via the sequential PT followed by DPT obtained at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of QM theory in the continuum with 3 ¼ 1 under normal conditions (see Fig. 1 Table 2).
Values of the Gibbs free energies of activation of the processes of the dipole-active tautomerization of the investigated A$T DNA base pairs are quite high and lie within the range 27-33 kcal mol À1 under normal conditions (Fig. 1, Table 1).
The A$T * O2 ðrw WC Þ, A$T*(rw WC ), A$T*(w H ), A$T * O2 ðw H Þ, A$T * O2 ðrw H Þ and A$T*(rw H ) base mispairs, which are the products of the mutagenic tautomerization of classical A$T DNA base pairs, represent themselves wobble structures with plane symmetric architecture (C s symmetry), stabilized by two antiparallel intermolecular H-bonds. They are noticeably more stable than the starting A$T(rWC), A$T(H) and A$T(rH) DNA base pairs and have quite high relative energies, lying in the range 19-28 kcal mol À1 , and hence -insignicant population (#1.2 Â 10 À14 under normal conditions). It is interesting to note, that these wobble base mispairs are guratively speaking "terminal stations" on the way of the mutagenic tautomerization of the investigated DNA base pairs, since they do not tautomerise further (Fig. 1, Tables 1 and 2).
Really, the A * N7 $Tðw H Þ and A * N7 $Tðrw H Þ complexes, which are formed from the A$T * O2 ðw H Þ and A$T*(rw H ) base pairs via the DPT, respectively, return without any barrier into the initial pairs due to the asynchronous DPT along the intermolecular Hbonds via the TS A$T*O2(wH)4A*N7$T(wH) and TS A$T*(rwH) 4A*N7$T(rwH) , accordingly. The same situation also takes place for the complex by the participation of the yilidic form 20 7 ps), which is formed from the A$T*(rw WC ) pair by the asynchronous DPT along the intermolecular H-bonds, is signicantly less than the time (10 À9 s) 27,28 , spent by the DNA-polymerase for the forced dissociation of the complementary pairs of the DNA bases into the monomers. As a result, this complex "slips out of its hands" and canonical tautomeric status of the A DNA base does not change (Table 1).
Base pairs remain plane symmetric structures during the entire PT and DPT tautomerization processes along the IRC. The methyl group of the T DNA base does not change its orientation during these tautomerization processes via the PT and DPT. Moreover, the heterocycles of the A and T DNA bases remain planar, despite their ability for the out-of-plane bending [130][131][132][133] (Fig. 1).
Interestingly, that the total energy of the intermolecular Hbonds only partially contributes to the electron energy of the monomers interactions among all without any exceptions Hbonded structures investigated in this work (see Fig. 1). In particular, in the TSs of mutagenic tautomerization, which are ion pairs, contribution of the H-bonds into the energy of their stabilization consist only 10-12% in comparison with the background of strong electrostatic (Coulomb) interactions. In other complexes it is much higherfrom 67 to 86% (Fig. 1). These regularities agree well with the previously reported data for the other H-bonded pairs of nucleotide bases. [31][32][33][34][35][36][37][38][39][40][41][42] Conclusions So, revealed microstructural mechanisms of the mutagenic tautomerization of the A$T DNA base pairs provide the generation of the mutagenic tautomers of only one among two DNA bases, in particular T DNA base, within the pair of bases. However, this generation is much more slower in comparison with the classical A$T(WC) DNA base pair and does not provide adequate population of the mutagenic tautomers (10 À9 to 10 À11 ).
Finally, these results lead us to a conclusion, which is very interesting from an evolutionary point of view: 6,80,81 among all classical pairs of the DNA bases only the Watson-Crick A$T(WC) DNA base pair can pretend on the role of the building block of the genetic material -DNA macromolecule with antiparallel strands, able for the self-development during large time intervals.

Conflicts of interest
There are no conicts to declare.