How many tautomerization pathways connect Watson–Crick-like G*·T DNA base mispair and wobble mismatches?

In this study, we have theoretically demonstrated the intrinsic ability of the wobble G·T(w)/G*·T*(w)/G·T(w1)/G·T(w2) and Watson–Crick-like G*·T(WC) DNA base mispairs to interconvert into each other via the DPT tautomerization. We have established that among all these transitions, only one single G·T(w) ↔ G*·T(WC) pathway is eligible from a biological perspective. It involves short-lived intermediate – the G·T*(WC) base mispair – and is governed by the planar, highly stable, and zwitterionic transition state stabilized by the participation of the unique pattern of the five intermolecular O6+H⋯O4−, O6+H⋯N3−, N1+H⋯N3−, N1+H⋯O2−, and N2+H⋯O2− H-bonds. This non-dissociative G·T(w) ↔ G*·T(WC) tautomerization occurs without opening of the pair: Bases within mispair remain connected by 14 different patterns of the specific intermolecular interactions that successively change each other along the IRC. Novel kinetically controlled mechanism of the thermodynamically non-equilibrium spontaneous point GT/TG incorporation errors has been suggested. The mutagenic effect of the analogues of the nucleotide bases, in particular 5-bromouracil, can be attributed to the decreasing of the barrier of the acquisition by the wobble pair containing these compounds of the enzymatically competent Watson–Crick’s geometry via the intrapair mutagenic tautomerization directly in the essentially hydrophobic recognition pocket of the replication DNA-polymerase machinery. Proposed approaches are able to explain experimental data, namely growth of the rate of the spontaneous point incorporation errors during DNA biosynthesis with increasing temperature.

Significant step in this biologically important direction has been performed in the pioneer work (Brovarets' & Hovorun, 2009a), where for the first time it was theoretically shown the unique ability of the wobble G·T(w) base pair, stabilized by two antiparallel N3H⋯O6 and N1H⋯O2 H-bonds, to transform through the dynamically unstable intermediatethe G·T*(WC) mismatchinto the G*·T(WC) DNA base mispair, which is the global minimum, and vice versa. Herewith the zwitterionic planar TS G þ ÁT À GÁTðwÞ$GÁTÃðWCÞ (" + " means protonation and "−" deprotonation of the G and T bases by the O6 and N3 sites, respectively), transition state of this conversion is stabilized by the participation of the original pattern of the five O6 + H⋯O4 -, O6 + H⋯N3 -, N1 + H⋯N3 -, N1 + H⋯O2 -, and N2 + H⋯O2 -H-bonds. Moreover, it was revealed (Brovarets', , 2013Brovarets' & Hovorun, 2009b) that the mutagenic tautomerization of the wobble G· 5 XU (w) (X = H, Me, F, Cl, Br) base pairs containing 5-halogen derivatives of the uracil ( 5 XU) possesses common nondissociative nature: In all cases, the planar, highly stable, and zwitterionic TS G þ Á 5 XU À GÁ 5 XUðwÞ$GÁ 5 XUÃðWCÞ transition state is stabilized by the participation of the one and the same unique scheme of the five intermolecular H-bonds during the G· 5 XU(w) ↔ G*· 5 XU(WC) tautomerization process, that is accompanied by a significant change in the base pair geometry. The Gibbs free energy of the forward barrier of the G· 5 XU(w) → G*· 5 XU(WC) tautomerization via the DPT falls into the range (MP2/6-311++G(2df, pd)// B3LYP/6-311++G(d, p)): T (17.51) > U (17.08) > 5 FU (15.49) > 5 ClU (15.39) > 5 BrU (15.35 kcal mol −1 under normal conditions) (Brovarets', 2013;Brovarets' & Hovorun, 2009b). It was also shown that the mutagenic tautomerization of the wobble G· 5 XU(w) base mispairs into the Watson-Crick-like G*· 5 XU(WC) mismatches proceeds much slower comparably with the time spent by the DNA-polymerase on the incorporation of one nucleotide into the structure of the DNA double helix (Duderstadtm, Reyes-Lamothe, van Oijen, & Sherratt, 2014;Kirmizialtin, Nguyen, Johnson, & Elber, 2012). It makes it possible to suggest a new kinetically controlled mechanism for the spontaneous point mutations occurrence, as well as for the mutagenesis induced by 5-halogen derivatives of the uracil .
As it turned out, barriers of the tautomerization of the wobble mismatches involving base analog mutagens into the Watson-Crick's mispairs decrease comparably with those obtained for the interconversion of the mispairs including canonical bases and thus provide higher frequency of the transitions (incorporation errors) induced by the mutagenic base analogs (Brovarets', , 2013Brovarets' & Hovorun, 2009b). This approach has also been found to be highly productive in clarifying the origin of the induced transitions: In particular, it was proved that the 5-halogen derivatives of the U base produce exceptionally incorporation errors .
In this study, we decided to raise again the topic of the spontaneous point mutations and to investigate more thoroughly all theoretically possible ways of the tautomerization events, comprising wobble and Watson-Crick pairs by the participation of the G and T bases both in the canonical and mutagenic tautomeric forms (Brovarets' & Hovorun, 2010bBrovarets', Zhurakivsky, & Hovorun, 2015), in view of the exceptional importance of these tautomerization processes in terms of the microstructural theory of the spontaneous point mutagenesis, which hitherto has not been created in its final and internally non-contradictable form.
The main goal of this work was to answer on the fundamental question, whether the biologically important pathway of the G·T(w) ↔ G*·T(WC) tautomeric transition presented for the first time in the work (Brovarets' & Hovorun, 2009a) is the sole. In this study, in addition to the already known G·T(w) ↔ G*·T(WC) tautomerization pathway (Brovarets' & Hovorun, 2009a), that has sparked a great interest last time (Bebenek, Pedersen, & Kunkel, 2011;Kimsey et al., 2015;Nomura et al., 2013;Kimsey, Petzold, Sathyamoorthy, Stein, & Al-Hashimi, 2015), we managed to reveal three new routes of the tautomerization, namely G*·T(WC) ↔ G·T(w 1 ), G*·T(WC) ↔ G·T (w 2 ), and G*·T(WC) ↔ G*·T*(w), occurring via the sequential DPT and rearrangement of the bases, respectively, each other within the pair and concerning a novel wobble structures formed by the G and T bases in their canonical and rare tautomeric forms (Brovarets', Yurenko, Dubey, & Hovorun, 2012), and to establish their structural, energetic and kinetic properties. A key finding of this work is that eventually it turned out that two novel uncovered G*·T(WC) ↔ G·T(w 1 ) and G*·T (WC) ↔ G·T(w 2 ) tautomerization reactions are too slow events comparably with the time of the DNA replication in the cell (see works (Alberts et al., 2002;Friedberg et al., 2006) and references therein) and the third one -G*·T(WC) ↔ G*·T*(w)is low probable, or, in other words, all of them are unrealistic and cannot be considered as an acceptable alternative to the path that was previously revealed (Brovarets' & Hovorun, 2009a). Possible biological implications for the results, which we obtained here and previously, have been also critically discussed in the brief form.
Reaction pathway was established by following intrinsic reaction coordinate (IRC) in the forward and reverse directions from each TS using Hessian-based predictorcorrector integration algorithm (Hratchian & Schlegel, 2005) with tight convergence criteria. These calculations eventually ensure that the proper reaction pathway, connecting the expected reactants and products on each side of the TS, has been found. We have investigated the evolution of the energetic, geometric, polar, and electrontopological characteristics of the H-bonds and base pairs along the pathway of the G·T(w) ↔ G*·T(WC) tautomerization reaction establishing them at the each point of the IRC , 2015bBrovarets' et al., 2013.
Electronic interaction energies E int have been calculated at the MP2/6-311++G(2df, pd)//B3LYP/6-311++G (d, p) level of theory as the difference between the total energy of the base mispair and the energies of the isolated monomers. Gibbs free energy of interaction has been obtained using similar equation. In each case, the interaction energy was corrected for the basis set superposition error (Boys & Bernardi, 1970;Gutowski, Van Lenthe, Verbeek, Van Duijneveldt, & Chałasinski, 1986) through the counterpoise procedure (Sordo, 2001;Sordo, Chin, & Sordo, 1988).
The Gibbs free energy G for all structures was obtained in the following way: where E elelectronic energy, while E corrthermal correction. We applied the standard TS theory (Atkins, 1998) to estimate activation barriers of the tautomerization reactions.
The time τ 99.9% necessary to reach 99.9% of the equilibrium concentration of the initial and terminal base mispairs in the system of reversible first-order forward (k f ) and reverse (k r ) reactions can be estimated by formula (Atkins, 1998): To estimate the values of the rate constants k f and k r , we applied standard TS theory (Atkins, 1998), in which quantum tunneling effect is accounted by Wigner's tunneling correction (Wigner, 1932), that has been successfully used for the DPT reactions : where k B -Boltzmann's constant, h -Planck's constant, ΔΔG f,r -Gibbs free energy of activation for the tautomerization reaction in the forward (f) and reverse (r) directions, ν imagnitude of the imaginary frequency associated with the vibrational mode at the TS. Bader's quantum theory of atoms in molecules was applied to analyze the electron density distribution (Bader, 1990;Lecomte, Espinosa, & Matta, 2015;Matta, 2014;Matta, Huang, & Massa, 2011). The topology of the electron density was analyzed using program package AIMAll (Keith, 2010) with all default options. The presence of a bond critical point (BCP), namely the so-called (3,−1) BCP, and a bond path between hydrogen donor and acceptor, as well as the positive value of the Laplacian at this BCP (Δρ > 0), were considered as criteria for the H-bond formation (Brovarets', Yurenko, & Hovorun, 2014a. Wave functions were obtained at the level of theory used for geometry optimization. The energies of the weak CH⋯O H-bonds  were calculated by the empirical Espinosa-Molins-Lecomte (EML) formula (Espinosa, Molins, & Lecomte, 1998;Mata, Alkorta, Espinosa, & Molins, 2011), which has been first successfully applied by Matta (Matta, Castillo, & Boyd, 2006) for the estimation of the individual energetic contributions of the separate H-bonds in the two Watson-Crick DNA base pairs: where V(r)value of a local potential energy at the (3, −1) BCP. The energies of the AH⋯B (A, B designate O, or N atoms) conventional H-bonds were evaluated by the empirical Iogansen's formula (Iogansen, 1999): where Δνmagnitude of the redshift (relative to the free molecule) of the stretching mode of the AH H-bonded group involved in the AH⋯B H-bond. The partial deuteration was applied to minimize the effect of vibrational resonances .
The energies of the OH⋯O and NH⋯O/N H-bonds in the selected TSs containing loosened covalent bridges were estimated by the Nikolaienko-Bulavin-Hovorun formulas (Nikolaienko, Bulavin, & Hovorun, 2012): where ρthe electron density at the (3, −1) BCP of the H-bond. The atomic numbering scheme for the G and T bases is conventional (Saenger, 1984).

Results and their discussion
Novel pathways of the tautomerization of the G*·T (WC) base mispair into the G·T(w 1 ) and G·T(w 2 ) wobble mismatches and vice versa In this study, for the first time, we have detected three additional ways of the tautomeric conversion of the Watson-Crick-like G*·T(WC) base mispair into the wobble G·T(w 1 ), G·T(w 2 ), and G*·T*(w) base mispairs and vice versa, that have not been presented in the literature by this time (Figures 1-10 and Tables 1-7). Let us analyze them one after another.
The second new route -G*·T(WC)↔G·T(w 1 ) (Tables 1, 2, 4, and Figures 1a, 3a, and 4), passing through the dynamically unstable intermediatethe G·T*(WC) base mispair (Brovarets' & Hovorun, 2015a;, occurs without opening of the pair that is tautomerized and is accompanied by the substantial changes in the base pair geometry. The G*·T(WC)↔G·T(w 1 ) tautomerization reaction includes two stagesvery fast one, from which the tautomerization process starts, and a very slow final phase. Tautomerization of the G*·T(WC) base pair begins with a very rapid process of the G*·T (WC)→G·T*(WC) DPT tautomerization (Table 3 and Figure 1a); at this, the G·T*(WC) base pair acts as a dynamically unstable intermediate (Brovarets' & Hovorun, 2015a;. Terminal, very slow (τ 99.9% = 2.31 × 10 8 s) stage of the G*·T (WC) → G·T(w 1 ) tautomerization passes (Figures 3a, 4, and Table 4) through the substantially non-planar zwitterionic TS G À ÁT þ GÁTÃðWCÞ$GÁTðw 1 Þ transition state (∠C6N1N3C5 = 83.7°) with the relative Gibbs free energy 32.28 kcal mol −1 (Table S1) under normal conditions and is stabilized by the participation of the two parallel H-bonds -O4 + H⋯N1 -(8.39) and N3 + H⋯N1 -(13.14 kcal mol −1 ) (Table 1, Figure 3a), which are centered on the one and the same N1nitrogen atom of the Gbase. The N9H and N1H glycosidic bonds of the Gand T + bases in the TS G À ÁT þ GÁTÃðWCÞ$GÁTðw 1 Þ are in the synorientation relatively each other (∠N9H 9 H 1 N1 = 67.6°). It is formed by the proton transfer from the N1 nitrogen atom of the G base along the intermolecular N1H⋯N3 H-bond to the N3 nitrogen atom of the T* base in the G·T*(WC) base mispair and is accompanied by the mutual rotation of the bases around the N1-N3 imaginary axis almost at a right angle. Vibrational spectra of the TS G À ÁT þ GÁTÃðWCÞ$GÁTðw 1 Þ contains mode with the imaginary frequency ν i = −674.7i cm −1 .
This tautomerization process results in the formation of the substantially non-planar (∠C6N1N3C5 = 87.7°) wobble G·T(w 1 ) base mispair, which is stabilized by three intermolecular C5 Me H⋯O6 (1.85), N1H⋯O4 (2.90), and N2H⋯O4 (0.71 kcal mol −1 ) H-bonds (Tables 1, 2, and Figure 3a). This tautomerization process is also accompanied by the significant change in the geometry of the base pair. However, at this, the base pair does not decompose into the monomers, remaining joined by the different patterns of the intermolecular H-bonds that successively change each other. To the best of our knowledge, the wobble G·T(w 1 ) DNA base mispair has not been mentioned in the literature so far. Cis-orientation of the N1H and N9H glycosidic bonds is characteristic for the wobble G·T(w 1 ) base pair (∠N9HHN1 = 39.7°). This pair can be easily planarized (ΔΔG TS = 1.23 kcal mol −1 ) by turning of the Me-group at an angle of 60°and a flattening of the NH 2 amino group of the G base ( Figure 3b). Only under this circumstance, the wobble G·T(w 1 ) base mispair can be incorporated into the DNA double helix. It should be noted that the low-energy wobble G·T (w 1 ) base mispair is connected with the high-energy wobble G·T(w 2 ) base mispair (ΔG = 1.16 kcal mol −1 under normal conditions) by the fast (τ 99.9% = 1.56 × 10 −11 s) conformational transformation (Table 4 and Figure 3c) via the substantially non-planar TS GÁTðw 1 Þ$GÁTðw 2 Þ transition state (∠C6N1N3C5 = 122.3°) stabilized by the N1H⋯O4 (1.98) and N2H⋯O4 (0.78 kcal mol −1 ) H-bonds (Table 1) that is centered on the one and the same O4 oxygen atom of the T base. This G•T(w 1 )↔G•T(w 2 ) conformational conversion corresponds to the vibrational mode with the imaginary frequency ν i = −15.2i cm −1 and occurs without opening of the pairbases remain bound by various H-bonds, which replace each other.
It is interesting to note that mirror-symmetric enantiomers of the G·T(w 2 ) base mispair (∠C6N1N3C5 = ± 62.8°), that is presented here for the first time and has not been published elsewhere in the literature before, interconvert between each other through the planar TS GÁTðw 2 Þ$GÁT sym ðw 2 Þ transition state (ΔΔG TS = 6.89 kcal mol −1 under normal conditions) (Table S2 and Figure 3d), to which corresponds the torsion vibration of the NH 2 group of the G base with imaginary frequency ν i = −178.2i cm −1 . This fast (τ 99.9% = 6.09 × 10 −8 s) (Table S2) and large amplitude quantum oscillation of the G·T(w 2 ) base mispair allows it to be incorporated into the structure of the DNA double helix, since its energy is significantly less than the energy of the stacking interactions of the neighboring Watson-Crick DNA base pairs (Jissy & Datta, 2014).
The third novel G*·T(WC) ↔ G·T(w 2 ) pathway (Table 5 and Figures 5 and 6) is controlled by the slightly non-planar (∠C6N1N3C5 = 13.5°) TS G À ÁT þ GÃÁTðWCÞ$GÁTðw 2 Þ transition state, that is an ion pair involving G − base, deprotonated by the N1 site, and T + base, protonated by the N3 site, stabilized by the participation of the four intermolecular O4 + H⋯O6 − (4.70), O4 + H⋯N1 − (5.19), N3 + H⋯N1 − (5.00), and N3 + H⋯N2 − (2.02 kcal mol −1 ) H-bonds (Table 1). The vibrational mode with imaginary frequency ν i = -291.2i cm −1 corresponds to it. The TS G À ÁT þ GÃÁTðWCÞ$GÁTðw 2 Þ transition state is formed by the transfer of the proton localized at the O6 oxygen atom of the G base along the intermolecular O6H⋯O4 H-bond to the O4 oxygen atom of the T base and is accompanied by the significant displacement of the bases relatively each other ( Figure 5). This very slow tautomerization process (τ 99.9% = 8.53 × 10 12 s) ( Table 5) is completed with the transition to the essentially non-planar wobble G·T(w 2 ) base pair, which is stabilized by three H-bonds: N1H⋯O4 (2.43) and N2H⋯O4 (1.89) with the joint centerthe O4 atom of the T baseand N3H⋯N2 (2.82 kcal mol −1 ) ( Table 1). The N9H and N1H glycosidic bonds of this base pair are in cis-orientation relative to each other (∠N9H 9 H 1 N1 = 57.1°). The G*·T (WC) ↔ G·T(w 2 ) tautomerization process described here is accompanied by the significant change in geometry of the pair that is tautomerized; at this, the pair does not decayit remains stabilized by the different patterns of the intermolecular H-bonds sequentially changing each other.
The data obtained in this study allow us to conclude that previously described biologically important route of the G•T(w) ↔ G·T*(WC) tautomerization (Brovarets' & Hovorun, 2009a) has no reasonable alternatives from the standpoint of the spontaneous point mutagenesis, since three new reaction paths that were discussed above -G*·T(WC) ↔ G·T(w 1 ), G*·T(WC) ↔ G·T(w 2 ), and G*·T(WC) ↔ G*·T*(w)are either much slower processes than even the process of the DNA replication in the cell (~10 6 s (Alberts et al., 2002;Friedberg et al., 2006)) (in the case of the G*·T(WC)↔G·T(w 1 ) and G*·T(WC)↔G·T(w 2 ) tautomerization reactions), or low probable (3.8 × 10 −10 ) (in the case of the G*·T (WC)↔G*·T*(w) pathway). However, in our opinion, these pathways take a keen interest in the study of the mechanisms of the mutagenic tautomerization of the other biologically important wobble pairs involving G and T nucleotide bases with the cognate architecture of the H-bonding.
Detailed microstructural information about the course of the G·T(w)↔G*·T(WC) tautomerization via the sequential DPT is presented in Figures 7, S2-S5 and Tables 6, 7.
Based on these data, we can arrive to the following important conclusions: (1) Both extrema of the first derivative of the electron energy with respect to the IRC -dE/dIRC ( Figure Table 7).
It is logical to suggest that the barrier of the G·T (w)→G*·T(WC) mutagenic tautomerization of the wobble G·T(w) base mispair in the recognition pocket of the DNA-polymerase reduces comparably with the isolated state, in particular, due to the stacking interactions (Jissy & Datta, 2014). At this, the values of the Gibbs free energy of the G*·T(WC) base mispair relatively to the G·T(w) mismatch together with just mentioned barrier The BSSE-corrected electronic interaction energy. b The total energy of the intermolecular H-bonds (see Table 1). c The BSSE-corrected Gibbs free energy of interaction (T=298.15 K). § and § § Data are taken from the works (Brovarets' & Hovorun, 2015a) and (Brovarets' & Hovorun, 2009a), respectively.  Figure S1). For definitions see Figure 1. also decrease comparably with the corresponding values in the isolated state due to the interaction of the invariant N3/O2 atomic groups of the G*·T(WC) base mispair with the appropriate amino acid residues of the recognition pocket of the high-fidelity DNA-polymerase (Brovarets' & Hovorun, 2015a;Poltev & Bruskov, 1977;Poltev, Shulyupina, & Bruskov, 1998). Oddly enough, but the replicative DNA-polymerase accelerates the G·T(w) → G*·T(WC) process of the acquisition by the wobble pair of the Watson-Crick geometry comparably with the isolated state. It is very eloquently that this tautomerization process occurs without the destruction of the pair (Figures 9 and  10) and hence without the direct participation in it of the endogenous water molecules as a chemical agent: This is due to the fact that tautomerization is controlled by the zwitterionic transition state TS G þ ÁT À GÁTðwÞ$GÁTÃðWCÞ , which energy of stabilization (ΔE int /ΔG int = −135.84/ 120.59 kcal mol −1 ) ( Table 2) is much greater than the energy of the bases hydration by the corresponding sites of the interaction (Danilov et al., 2009;Furmanchuk et al., 2011;Zubatiuk, Shishkin, Gorb, Hovorun, & Leszczynski, 2015). Incidentally, the base pair, that is tautomerized, stays in the zwitterionic state in the fairly wide range of the IRC values: −5.20 to 10.14 Bohr.  Figure S1 in the Supplementary Files for the profile of the relative electronic energy ΔE of the G·T (w 2 ) ↔ G·T sym (w 2 ) conformational interconversion of the mirror-symmetric enantiomers of the wobble G·T(w 2 ) base mispair via the rotation of the NH 2 amino group of the G base along the IRC obtained at the B3LYP/6-311++G(d, p) level of theory. Table 3. Energetic and kinetic characteristics of the G*·T(WC) ↔ G·T*(WC) (Brovarets' & Hovorun, 2015a), G·T* (WC) ↔ G + ·T − (w) and G + ·T − (w) ↔ G*·T*(w) tautomerization reactions obtained at the different levels of theory for the geometry calculated at the B3LYP/6-311++G(d, p) level of theory.  The Gibbs free energy of the product relatively the reactant of the tautomerization reaction (T = 298.15 K), kcal mol −1 . b The electronic energy of the product relatively the reactant of the tautomerization reaction, kcal mol −1 .

Level of theory
c The Gibbs free energy barrier for the forward reaction of tautomerization, kcal mol −1 . d The electronic energy barrier for the forward reaction of tautomerization, kcal mol −1.
e The Gibbs free energy barrier for the reverse reaction of tautomerization, kcal mol −1 . f The electronic energy barrier for the reverse reaction of tautomerization, kcal mol −1 . g The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerization reaction, s. See also summary Table S1 for the Gibbs and electronic energies of the mispairs and TSs relatively the global minimumthe Watson-Crick-like G*·T(WC) base mispair.
Since the characteristic parameter τ 99.9% of the G•T (w) ↔ G•T*(WC) tautomerization (2.42 s (Table 6)) is much greater than the time Δt pol = 8.3 × 10 −4 s, which spends DNA-polymerase machinery for the one act of incorporation of the incoming nucleotide into the structure of the DNA double helix that is synthesized (Kirmizialtin et al., 2012), it implies with necessity that the emergence of the spontaneous transitionsthermodynamically non-equilibrium incorporation errorsis under the kinetic control. This observation automatically explains the well-known experimental factthe growth of the rate of the spontaneous point mutations (as it is known, transitions make up the bulk among them Friedberg et al., 2006;Lee Table 4. Energetic and kinetic characteristics of the G·T*(WC) ↔ G·T(w 1 ) tautomerization reaction and G·T(w 1 ) ↔ G·T(w 2 ) conformation transition obtained at the different levels of theory for the geometry calculated at the B3LYP/6-311++G(d, p) level of theory. Note: For footnote definitions see Table 3.     Lynch, 2010)) with increasing temperature (see Refs. (Auerbach, 1976;Lindgren, 1972) and bibliography presented there).

Level of theory
Most interesting fact follows from the phenomenon of the kinetic control of the spontaneous point mutations, namely GT/TG incorporation errors: If from one or another reason DNA-polymerase machinery as a part of replisome (Ligasová & Koberna, 2011) slows its operation (time Δt pol increases), it once again automatically leads to the increasing of the frequency of the spontaneous transitions. In this way, in particular, the nature of the so-called error catastrophe (Li et al., 2014) can be explained.
Further, since endogenous water is not directly included in the processes of the mutagenic tautomerization that underlie the occurrence of the spontaneous transitionsincorporation errors, so the dependency of the frequency of the latters on pH can be explained by the immediate influence of this physico-chemical factor per se on the course of the G·T(w)→G*·T(WC) tautomerization reaction, that is controlled by the zwitterionic transition state TS G þ ÁT À GÁTðwÞ$GÁTÃðWCÞ , but not only by the ionization of the isolated bases, incorporated into these pairs (Koag, Nam, & Lee, 2015).
By the way, comparison of our data, including lengths of the intermolecular H-bonds, with experimental data (Bebenek et al., 2011) unequivocally testifies to the fact that exactly the quasi-planar G*·T(WC) base mispair is enzymatically competent base pair, but not the others possible G·T*(WC) (Brovarets' & Hovorun, 2015a), G -·T, or G·Tpseudo-Watson-Crick mispairs (Brovarets', Zhurakivsky, & Hovorun, 2010), since namely for it the best coincidence of the theoretical results with experimental data is observed (see Table 6 in Brovarets' & Hovorun, 2015a).
And finally the latter. It is completely logical to associate the mutagenic action of the modified nucleotide bases with the reduction of the energetic barrier of the tautomerization of the wobble mispairs into the Watson-Crick mispairs by their participation within the Table 6. Energetic and kinetic characteristics of the G·T(w) ↔ G·T*(WC) (Brovarets' & Hovorun, 2009a) and G·T*(WC) ↔ G*·T (WC) (Brovarets' & Hovorun, 2015a)    framework of the proposed model of the origin of the spontaneous transitionsincorporation errors. Indeed, the probability P of the origin of the spontaneous transitionsincorporation errorscan be estimated by the formula P = P w ·P w → WC , where P wthe probability of the wobble base mispair formation in the recognition pocket of the replicative DNA-polymerase and P w → WCthe probability of the conversion of the wobble base mispair into the Watson-Crick-like base mispair in the recognition pocket of the replicative DNA-polymerase. Whereas both multipliers included to this formula, especially P w → WC , are much smaller than 1, so the low frequency of the spontaneous point mutationsincorporation errorscan be explained by this fact.
Unfortunately, experimental values of the P w and P w → WC parameters are not available in the literature now. However, the growth of the rate of the transitions induced by the modification of the bases P ind /P spont = P w → WC /P w → WC (the titles of the pairs involving modified bases-mutagens are highlighted in bold) can be estimated by this formula in the first approximation. An elementary calculation of the P ind /P spont ratio by the known formulas of the physico-chemical kinetics (Podolyan, Gorb, & Leszczynski, 2003) using numerical data for the corresponding values of the reaction rates (k f = 0.97/k r = 0.39 s −1 for the G·T(w) → G*·T(WC) tautomerization (Brovarets' & Hovorun, 2009a) and k f = 34.20/k r = 19.59 s −1 for the G· 5 BrU(w)→G*· 5 BrU (WC) tautomerization (Brovarets', , 2013Brovarets' & Hovorun, 2009b); Δt pol = 8.3 × 10 −4 s (Kirmizialtin et al., 2012)) gives the value equals to 35, which despite the simplified model agrees well with experimental data which constitute from 20 (Lasken & Goodman, 1985) to 29 (Kaufman & Davidson, 1978) times. This is the convincing evidence of the adequacy of the proposed and substantiated by us microstructural model of the emergence of the spontaneous, as well as induced by the modified nucleotide bases incorporation errors that occur during DNA biosynthesis.

Conclusions and perspectives
To the best of our knowledge, this study is the first report, where it was revealed for the first time that biologically important process of the G·T(w) ↔ G*·T(WC) mutagenic tautomerization is carried out by one single route, controlled by the zwitterionic planar transition state TS G þ ÁT À GÁTðwÞ$GÁTÃðWCÞ , which is stabilized by the participation of the unique pattern of the five intermolecular H-bonds. The G·T(w) ↔ G*·T(WC) tautomerization process Figure 9. Profiles of the E AH⋯B energies of the intermolecular H-bonds estimated by the EML formula at the (3, −1) BCPs along the IRC of the G·T(w) ↔ G*·T(WC) tautomerization via the sequential DPT obtained at the B3LYP/6-311++G(d, p) level of theory (see Tables 1 and 7). Figure 10. Profiles of: (a) the distance R(H 1 -H 9 ) between the H 1 and H 9 glycosidic hydrogens of the T and G bases, respectively, and (b) the α 1 (∠N9H 9 (G)H 1 (T)) and α 2 (∠N1H 1 (T)H 9 (G)) glycosidic angles along the IRC of the G·T(w)↔G*·T(WC) tautomerization via the sequential DPT obtained at the B3LYP/6-311++G(d, p) level of theory (see Figure 7). occurs without opening of the pair, that tautomerizes, and ensures the acquisition by the wobble G·T(w) base pair of the geometric mimicry with the Watson-Crick base pair. This means that this process is intrapair (i.e., in this case, Nature exploits the ability of the wobble G·T(w) base pair to tautomerize spontaneously in the process of thermal fluctuations into the G*·T(WC) base mispair with Watson-Crick geometry as its immanency) and therefore does not require for its implementation the endogenous water molecules. In the previously studied systems, water affects the tautomerization process intervening directly into the process itself (Danilov et al., 2009;Furmanchuk et al., 2011;Zubatiuk et al., 2015). Throughout the entire G·T(w)↔G*·T(WC) tautomerization process bases within pairs remain connected by 14 different patterns of the intermolecular interactions including from 2 to 5 AH⋯B H-bonds and 3 loosened A-H-B covalent bridges that successively change each other along the IRC.
In the course of the G·T(w) → G·T*(WC) intermolecular mutagenic tautomerization G base as a molecule-partner of interaction plays the role of the catalyst, significantly accelerating this reaction in comparison with the intramolecular mutagenic tautomerization of the T base. At this, the ΔΔG TS Gibbs free energy barrier of the tautomerization is reduced to 17.47 kcal mol −1 (Table 7), when T base tautomerizes via the intermolecular DPT within the G·T(w) base pair, in comparison with the tautomerization within the isolated base via the intramolecular SPT, for which this value is 39.22 kcal mol −1 under normal conditions (Brovarets' & Hovorun, 2010a).
In this study, novel kinetically controlled mechanism of the spontaneous point mutationsincorporation errors that are thermodynamically non-equilibrium events has been suggested.
Moreover, in the framework of this model, the nature of the mutagenic activity of the 5 XU (X = F, Cl, Br) compounds becomes clear: It is connected with the decreasing of the barrier of the G· 5 XU(w)→G· 5 XU*(WC) tautomerization reaction. Simple estimation by the formulas of the physico-chemical kinetics (Podolyan et al., 2003) gives a value equal to 7.9 × 10 −4 and 2.8 × 10 −2 for the frequencies of the GT and G 5 BrU incorporation errors, respectively. At this, it was established that 5 BrU as the most strong mutagen among halogen derivatives of the U provides the exceeding of the background value corresponding to the T base in 35 times, that coincide well with the experimental data (Kaufman & Davidson, 1978;Lasken & Goodman, 1985).
Proposed approaches are able to explain quite naturally the growth of the rate of the spontaneous transitions with increasing temperature (Auerbach, 1976;Lindgren, 1972).
Discoveries presented above give impetus to a variety of implications for future investigations in the field of the spontaneous and induced point mutations and their reparation. Notably, the outlined theoretical concepts of the mutagenic tautomerization of the wobble G·T(w) base pair as its intrinsic property into the G*·T (WC) base pair with Watson-Crick geometry (Brovarets' & Hovorun, 2015a) have not only outstripped the experiment (Kimsey et al., 2015) by a few years, but also allowed to reasonably plan and interpret it.
Based on the theoretical data that have worthily passed the experimental verification of their viability, we can assume that reparation enzymes, "sharpened" for the wobble G·T(w) base mispair, cannot cope completely with their intended purpose. The point is that the instrinsic ability of this mismatch to switch into the G*·T(WC) base mispair with Watson-Crick geometry, representing itself "hiding place" from the enzyme that cannot be recognized by it, principally restricts the ultimate accuracy of the reparation process. Obviously, this assumption requires further experimental confirmation.
In addition, the foregoing discussion in principle allows to understand the mechanism according to which the G* mutagenic tautomer, which in themselves is a long-lived structure with a lifetime (Brovarets' & Hovorun, 2010a) that is by orders of magnitude greater than the time of the DNA replication in the cell (~10 6 s (Alberts et al., 2002;Friedberg et al., 2006)), can be eliminated from the genome. It is important to mention here once again, that the intrinsic ability of the G*·T (WC) base mispair to transform into the wobble G·T(w) base mispair allows to eliminate the G* tautomers from the genome by the reparation systems, "sharpened" for the G·T(w) base pair, by several cycles of DNA replication.
Results obtained in our present and previous studies (Brovarets', , 2013Brovarets' & Hovorun, 2009a, 2009b, 2015c are able to drastically change the existing conceptions according the general mechanisms of the origin of the spontaneous point mutations as at the DNA replication, so at the protein synthesis. We anticipate that our results would significantly influence the comprehension of the universal microstructural principles of the regulation of the DNA replication and transcription.

Supplementary material
The supplementary material for this paper is available online at http://dx.doi.org/10.1080/07391102.2015.1046936.
Technologies, Taras Shevchenko National University of Kyiv) and Dr Fernando R. Clemente (Gaussian, Inc.) for their technical support of the work.

Disclosure statement
No potential conflict of interest was reported by the authors.