Novel physico-chemical mechanism of the mutagenic tautomerisation of the Watson–Crick-like A·G and C·T DNA base mispairs: a quantum-chemical picture

Abstract

The newly discovered physico-chemical mechanism of the mutagenic tautomerisation of the long A·G and short C·T Watson–Crick DNA base mispairs was revealed for the first time. The tautomerisation of each mismatch occurs via four topologically and energetically different ways through highly stable transition states – H-bonded tight ion pairs containing protonated and deprotonated bases. These processes are accompanied by a significant rebuilding of the base mispairs with a Watson–Crick architecture into wobble mismatches, which are shifted towards both the minor and major DNA grooves and vice versa. Moreover, it was established that these tautomerisation reactions occur non-dissociatively and are accompanied by the consequent replacement of the unique patterns of the specific intermolecular interactions along the IRC. Finally, we briefly discuss the possible biological significance of the obtained results for clarifying the microstructural foundations of the origin of the spontaneous point mutations within the framework of the classical Watson–Crick tautomeric hypothesis.

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Introduction

A special place among all incorrect DNA base pairs – the “culprits” of the occurrence of spontaneous point mutations^1–4 – is occupied by two base pairs – the so-called long A·G and short C·T^5–12 pairs with the Watson–Crick molecular architecture of the binding between the bases.^13,14 The DNA bases that form the A·G and C·T DNA base mispairs are in the main tautomeric form,^15–17 in contrast to the other mispairs. Notably, the extension efficiencies for the mismatched base pairs presented by M. Goodman et al.¹⁸ constitute 10⁻⁴ to 10⁻⁵/10⁻² for the C(template)·T(primer)/T·C mispairs, respectively; while for the G·A/A·G mismatches, they are less than 10⁻⁶, compared to the canonical A·T Watson–Crick DNA base pair.

We have previously investigated in detail the process of the DPT tautomerisation of these pairs as their intrinsic property,^11,12 which is important in terms of the fixation of the mutations in the subsequent rounds of DNA replication. As a result, we have concluded that dissociation of the Watson–Crick-like A·G¹¹ and C·T¹² mispairs into the isolated monomers by DNA replication machinery proceeds without the changing of their tautomeric status. However, this conclusion is valid if, and only if, the DPT tautomerisation of the aforementioned pairs occurs via the classical Löwdin mechanism.^19,20

In this paper, we describe for the first time a new mechanism for the mutagenic tautomerisation, which combines a proton transfer and the shifting of the bases relative to each other of the long A·G and short C·T DNA base mispairs with a Watson–Crick (WC) architecture. During this tautomeric conversion, the Watson–Crick-like base pairs undergo large-scale structural changes to adopt a wobble (w) geometry. The characteristic difference of this novel mechanism from Löwdin’s mechanism consists of the fact that the mutagenic tautomerisation of the pairs is accompanied by significant changes in their geometry, namely by the transition into the wobble configuration, and is carried out through the highly stable transition states (TS)^21,22 A⁺·G⁻, A⁻·G⁺, C⁺·T⁻ and C⁻·T⁺ (signs “+” and “−” denote protonated and deprotonated DNA bases, respectively). The obtained data shed light on the nature of the spontaneous point A·G/G·A and C·T/T·C replication errors in DNA, when for one reason or another^13,14,19,20 complementary DNA bases randomly change their canonical tautomeric status into a mutagenic status during DNA replication. The results presented in this paper can broaden our outlook and provide valuable insights into the mechanisms of the origin of the spontaneous point replication errors at the atomistic level.

Computational methods

All calculations of the geometries and harmonic vibrational frequencies of the considered base mispairs and the transition states of their conversion have been performed using the Gaussian’09 package²³ at the DFT B3LYP/6-311++G(d,p) level of theory,^24–26 that has been applied for analogous systems and verified to give accurate geometrical structures, normal mode frequencies, barrier heights and characteristics of intermolecular H-bonds.^27,28 A scaling factor that is equal to 0.9668 has been applied in the present work for the correction of the harmonic frequencies of all the studied base pairs.^29–31 We have confirmed the minima and TS, located by means of a Synchronous Transit-guided Quasi-Newton method,³² on the potential energy landscape by the absence or presence, respectively, of the imaginary frequency in the vibrational spectra of the complex.

In order to consider the electronic correlation effects as accurately as possible, we followed geometry optimizations with single point energy calculations using the MP2 level of theory³³ and a wide variety of basis sets, in particular, Pople’s basis sets of valence triple-ζ quality,^34,35 as well as Dunning’s cc-type basis sets,³⁶ augmented with polarization and/or diffuse functions: 6-311++G(2df,pd), 6-311++G(3df,2pd), cc-pVTZ and cc-pVQZ.

The reaction pathways have been established by following the intrinsic reaction coordinate (IRC) in the forward and reverse directions from each TS using a Hessian-based predictor–corrector integration algorithm^37,38 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 and geometric characteristics of the H-bonds and base pairs along the reaction pathway, establishing them at each point of the IRC.^28,29

The electronic interaction energies, E_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 mispair and the energies of the isolated monomers. The Gibbs free energy of interaction has been obtained using a similar equation. In each case the interaction energy was corrected for the basis set superposition error (BSSE)^39,40 through the counterpoise procedure.^41,42

The Gibbs free energy, G, for all structures was obtained in the following way:

G = E_el + E_corr, (1)

where E_el = the electronic energy, while E_corr = the thermal correction.

We applied the standard TS theory⁴³ to estimate the activation barriers of the tautomerisation reaction.

The time τ_99.9% necessary to reach 99.9% of the equilibrium concentration of the reactant and product in the system of reversible first-order forward (k_f) and reverse (k_r) reactions can be estimated by the formula:⁴³

To estimate the values of the rate constants k_f and k_r:

we applied standard TS theory,⁴³ in which the quantum tunneling effect is accounted for by Wigner’s tunneling correction,⁴⁴ that has been successfully used for the DPT reactions:^45–47where k_B = Boltzmann’s constant, h = Planck’s constant, ΔΔG_f,r = the Gibbs free energy of activation for the tautomerisation reaction in the forward (f) and reverse (r) directions, and ν_i = the magnitude of the imaginary frequency associated with the vibrational mode at the TSs.

Bader’s Quantum Theory of Atoms in Molecules (QTAIM) was applied to analyse the electron density distribution.⁴⁸ The topology of the electron density was analysed using the AIMAll program package⁴⁹ with all default options. The presence of a bond critical point (BCP), namely the so-called (3,−1) BCP, and a bond path between the 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.^50,51 Wave functions were obtained at the level of theory used for geometry optimisation.

The energies of the N2H⋯HC2 dihydrogen (DH)-bond^11,52 in the A·G(WC) base mispair, the N2⁺H⋯HC2⁻ DH-bond in the TS^A−·G+_{A·G(WC)↔A*·G↓(w)} transition state, the weak C2H⋯O6 H-bond in the A*·G_↓(w) mismatch, the attractive¹² O2⋯O2 van der Waals vdW contacts in the C·T(WC), C*·T*(WC) base mispairs and the TS_{C·T(WC)↔C*·T*(WC)} transition state, and also the attractive¹² O2⁺⋯N3⁻ van der Waals contact in the TS^C−·T+_{C·T(WC)↔C·T*↑(w)} transition state were calculated by the empirical Espinosa–Molins–Lecomte (EML) formula^53,54 based on the electron density distribution at the (3,−1) BCPs of the specific contacts:

E_{NH⋯HC/N⁺H⋯HC⁻/CH⋯O/O⋯O/O⁺⋯N⁻} = 0.5V(r), (5)

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

The energies of the N4H⋯N3 and N3H⋯N3 H-bonds in the TS_{C*·T↑(w)↔C·T*O2(w)} and TS_{C·T(WC)↔C*·T*(WC)} transition states, respectively, containing loosened covalent bridges were estimated by the Nikolaienko–Bulavin–Hovorun formula:⁵⁵

E_NH⋯N = −2.03 + 225ρ, (6)

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

The energies of all the other AH⋯B conventional H-bonds were evaluated by the empirical Iogansen formula:⁵⁶

where Δν = the magnitude of the frequency shift of the stretching mode of the AH H-bonded group involved in the AH⋯B H-bond, relative to the unbound group. Partial deuteration was applied to minimize the effect of vibrational resonances.^45,46

One and the same values of the frequency (ν) and the distance shifts (d_AH) have been observed for the different H-bonds in the TS^C−·T+_{C·T(WC)↔C*·T↓(w)} and TS^C+·T−_{C*·T*(WC)↔C*·T↑(w)} transition states, since they involve joint O4⁺H/N3⁺H/N4⁺H donor groups. The same data have been observed for the various H-bonds in the TS^A+·G−_{A·G(WC)↔A*·G↑(w)} and TS^A+·G−_{A·G(WC)→A·G*↓(w)} transition states containing mutual N6⁺H/N1⁺H donor groups.

The atomic numbering scheme for the DNA bases is conventional.⁵⁷

Results and their discussion

First of all, before proceeding to the presentation of the obtained results and their discussion, we would like to generally outline the ideas which have encouraged us for the discovery of the new mechanism of the mutagenic tautomerisation via the sequential DPT accompanied with structural rearrangements of the DNA bases within the A·G and C·T base mispairs with Watson–Crick-type of H-bonding. It is known for certain that canonical DNA bases – adenine (A), guanine (G), cytosine (C) and thymine (T) – are able, in principle, to transfer from the canonical into the mutagenic tautomeric form by intramolecular migration of the amino proton of the A and C bases to the neighboring N1 or N3 nitrogen atoms, respectively, or by intramolecular migration of the imino proton of the G and T bases to the neighboring O6 and O4 oxygen atoms, respectively.^58–64 However, these tautomeric transitions occur quite slowly (∼10¹⁰ to 10²⁰ s), even in comparison with the time of DNA replication in the cell (∼10⁶ s (ref. 65 and 66)), since very high activation energy barriers (32–46 kcal mol⁻¹) correspond to such conversions.^58,60,63,64 We have hypothesized^21,22 that each of the canonical DNA bases in the considered A·G and C·T DNA base mispairs can catalyze the mutagenic tautomerisation of the “complementary” base, firstly by removing the migrating proton, then shifting relative to the other base within the base pair into the major or minor groove sides of the DNA helix and adding this mobile or other acidic proton to the neighboring nitrogen or oxygen atoms of the “complementary” base. It is quite natural to expect that the transition states of these processes would represent highly stable structures themselves,^21,22 namely the A⁺·G⁻, A⁻·G⁺, C⁺·T⁻ and C⁻·T⁺ H-bonded tight ion pairs, the geometry of which is no longer Watson–Crick, but is not yet wobble.

1. Mutagenic tautomerisation of the long A·G Watson–Crick DNA base mispair

The tautomerisation processes of this long pair induce the transfer of both the A and G bases (but independently from each other) into the mutagenic A* and G* tautomeric forms, accordingly: as a result of this, four different H-bonded A·G*_↓(w), A·G*_↑(w), A*·G_↓(w) and A*·G_↑(w) pairs with wobble architecture are formed (Fig. 1). This number of tautomerised pairs is not accidental – on the one hand, it is associated with the number of the acidic protons in each base pair, that are able to migrate one after another from one base to another (two of them represent the amino proton at the N6 nitrogen atom of the A base and the imino proton at the N1 nitrogen atom of the G base) forming in such a way through a highly stable structure corresponding to the TS, and, on the other hand, with the number of the terminal, tautomerised wobble configurations involving the mutagenic tautomers (this amount – 2 – can be also explained by the number of the DNA grooves, where one of the bases may shift relative to the other base during this process of mutagenic tautomerisation).

Fig. 1 Structures corresponding to the stationary points on the reaction pathways of the (a) A·G(WC) ↔ A·G*_↓(w), (b) A·G(WC) ↔ A·G*_↑(w), (c) A·G(WC) ↔ A*·G_↑(w) and (d) A·G(WC) ↔ A*·G_↓(w) conversions via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory. The dotted lines indicate AH⋯B H-bonds and AH⋯HB DH-bonds (their lengths are presented in angstroms). Carbon atoms are in light-blue, nitrogen in dark-blue, hydrogen in grey and oxygen in red. ν_i = imaginary frequency.

Among the two different pathways of the mutagenic tautomerisation of the A·G(WC) DNA base mispair, in particular A·G(WC) ↔ A·G*_↓(w) and A·G(WC) ↔ A·G*_↑(w), the first of them is much faster than the other and therefore is attractive from the biological point of view (Fig. 1 and 2 and Tables 1, 2, S1 and S2†). This A·G(WC) ↔ A·G*_↓(w) tautomeric conversion is initiated by the proton transfer at the N1 nitrogen atom of the G base along the intermolecular N1H⋯N1 H-bond to the N1 nitrogen atom of the A base. The TS^A+·G−_{A·G(WC)↔A·G*↓(w)} transition state, stabilized by the N6⁺H⋯O6⁻ (7.46), N1⁺H⋯O6⁻ (4.21) and N1⁺H⋯N1⁻ (2.96 kcal mol⁻¹) H-bonds in addition to the strong electrostatic interactions (Table S2†), possesses a wobble-like configuration due to the displacement of the deprotonated G⁻ base relative to the A⁺ base to the side of the DNA minor groove. The A·G*_↓(w) tautomerised base pair formed within this route has a shifted configuration and is stabilized by two N6H⋯O6 (1.64) and O6H⋯N1 (8.19 kcal mol⁻¹) H-bonds. Interestingly, herewith the O6H hydroxyl group of the G* base plays simultaneously the role of the donor as well as the acceptor of the H-bonding (Table 1).

Fig. 2 Profiles of the relative electronic energy, ΔE, of the DNA base mispairs along the IRC of the (a) A·G(WC) ↔ A·G*_↓(w), (b) A·G(WC) ↔ A·G*_↑(w), (c) A·G(WC) ↔ A*·G_↑(w) and (d) A·G(WC) ↔ A*·G_↓(w) tautomerisations via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory.

Table 1 Electron-topological, structural, vibrational and energetic characteristics of the intermolecular H-bonds and DH-bonds in the DNA base mispairs containing A and G nucleobases and TSs of their tautomerisation via the sequential DPT and structural displacement of the A and G bases relative to each other; the energetic and polar characteristics of the latter are obtained at the B3LYP/6-311++G(d,p) level of theory

Base pair/TS	AH⋯B H-bond/DH-bond	ρ^a	Δρ^b	100ε^c	dA⋯B^d	dH⋯B^e	ΔdAH^f	∠AH⋯B^g	Δν^h	EAH⋯B^i	ΔG^j	μ^k
a The electron density at the (3,−1) BCP of the H-bond, a.u.b The Laplacian of the electron density at the (3,−1) BCP of the H-bond, a.u.c The ellipticity at the (3,−1) BCP of the H-bond.d The distance between the A (H-bond donor) and B (H-bond acceptor) atoms of the AH⋯B H-bond, Å.e The distance between the H and B atoms of the AH⋯B H-bond, Å.f The elongation of the H-bond donating group AH upon AH⋯B H-bonding, Å.g The H-bond angle, degree.h The redshift of the stretching vibrational mode ν(AH) of the AH H-bonded group, cm^−1.i Energy of the H-bonds, calculated by Iogansen’s,^56 or Espinosa–Molins–Lecomte (marked with an asterisk)^53,54 formulas, kcal mol^−1.j The relative Gibbs free energy of the complex obtained at the MP2/cc-pVQZ//B3LYP/6-311++G(d,p) level of theory under normal conditions, kcal mol^−1.k The dipole moment of the complex, D.l Data are taken from the literature.^11
A·G(WC)^l	N6H⋯O6	0.032	0.109	3.79	2.866	1.842	0.019	176.6	336.2	5.68	0.00	5.21
	N1H⋯N1	0.032	0.084	6.64	2.972	1.936	0.024	178.9	429.1	6.51
	N2H⋯HC2	0.004	0.014	33.40	3.153	2.469	0.00007	124.6	−0.5	0.68*
A·G*↓(w)	N6H⋯O6	0.012	0.048	5.41	3.043	2.246	0.004	134.6	64.6	1.64	3.76	2.39
	O6H⋯N1	0.047	0.103	4.89	2.695	1.755	0.034	154.5	655.8	8.19
A·G*↑(w)	N6H⋯N1	0.023	0.070	6.74	3.083	2.065	0.014	176.0	255.8	4.85	6.28	2.87
	N2H⋯N1	0.024	0.073	7.10	3.061	2.046	0.014	172.6	258.0	4.87
A*·G↑(w)	N1H⋯N6	0.020	0.059	6.20	3.087	2.157	0.010	150.3	173.1	3.81	14.29	8.38
	N2H⋯N6	0.021	0.065	6.58	2.991	2.154	0.011	138.0	183.0	3.95
	N1H⋯N2	0.017	0.051	10.26	3.136	2.230	0.008	147.2	136.7	3.24
TS^A+·G−A·G(WC)↔A·G*↓(w)	N6^+H⋯O6^−	0.048	0.162	5.72	2.605	1.648	0.034	150.2	551.2	7.46	17.01	9.26
	N1^+H⋯O6^−	0.029	0.091	10.22	2.800	1.946	0.033	136.4	512.3	4.21
	N1^+H⋯N1^−	0.023	0.072	18.76	3.011	2.045	0.033	152.1	512.3	2.96
A*·G↓(w)	N1H⋯O6	0.015	0.057	0.81	2.973	2.185	0.005	132.9	71.5	1.85	21.11	9.54
	C2H⋯O6	0.009	0.034	25.94	3.146	2.488	−0.002	118.0	−29.4	1.75*
TS^A+·G−A·G(WC)↔A*·G↑(w)	N6^+H⋯O6^−	0.018	0.064	72.04	2.945	2.150	0.031	131.6	551.2	2.53	25.29	12.56
	N6^+H⋯N1^−	0.033	0.091	2.01	2.866	1.904	0.031	152.3	551.2	4.94
	N1^+H⋯N1^−	0.014	0.049	99.24	3.131	2.324	0.023	133.7	512.3	2.29
	N1^+H⋯N2^−	0.028	0.076	2.49	2.984	1.981	0.023	150.2	512.3	4.88
TS^A−·G+A·G(WC)↔A·G*↑(w)	O6^+H⋯N6^−	0.050	0.090	7.51	2.719	1.740	0.055	158.9	1005.1	10.25	25.79	5.29
	N1^+H⋯N6^−	0.068	0.093	7.94	2.642	1.617	0.071	155.5	1067.3	10.58
	N2^+H⋯N1^−	0.024	0.065	7.48	3.063	2.089	0.021	157.3	345.8	5.77
TS^A−·G+A·G(WC)↔A*·G↓(w)	O6^+H⋯N1^−	0.056	0.079	2.79	2.715	1.686	0.078	167.3	1330.8	11.86	49.20	12.87
	N1^+H⋯N1^−	0.021	0.071	16.40	2.988	2.106	0.008	143.2	123.3	3.01
	N2^+H⋯HC2^−	0.005	0.016	36.78	3.083	2.277	0.0004	136.1	10.0	0.85*

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Among the two other tautomerisation pathways (Tables 1, 2, S1 and S2† and Fig. 1 and 2), namely A·G(WC) → A*·G_↑(w) and A·G(WC) → A*·G_↓(w), the second of them is extremely slow, even in comparison with the time of DNA replication in the cell (∼10⁶ s (ref. 65 and 66)) and so it does not have actual biological meaning. The first A·G(WC) → A*·G_↑(w) tautomerisation process starts with the migration of the proton localized at the N1 nitrogen atom of the G base along the intermolecular N1H⋯N1 H-bond to the N1 nitrogen atom of the A base. The TS^A+·G−_{A·G(WC)↔A*·G↑(w)} transition state, stabilized by the N6⁺H⋯O6⁻ (2.53), N6⁺H⋯N1⁻ (4.94), N1⁺H⋯N1⁻ (2.29) and N1⁺H⋯N2⁻ (4.88 kcal mol⁻¹) H-bonds along with the strong electrostatic interactions (Table S2†), as well as the tautomerised A*·G_↑(w) DNA base mispair, joined by the N1H⋯N2 (3.24), N1H⋯N6 (3.81) and N2H⋯N6 (3.95 kcal mol⁻¹) H-bonds, have wobble configurations due to the displacement of the deprotonated G⁻ base relative to the A⁺ base towards the DNA major groove (Table 1).

Table 2 Energetic and kinetic characteristics of the A·G(WC) ↔ A·G*_↓(w), A·G(WC) ↔ A·G*_↑(w), A·G(WC) ↔ A*·G_↑(w) and A·G(WC) ↔ A*·G_↓(w) tautomerisations via the sequential DPT obtained at different levels of theory for the geometry calculated at the B3LYP/6-311++G(d,p) level of theory (see also Fig. 1 and Table S1)^h

Level of theory	ΔG^a	ΔE^b	ΔΔGTS^c	ΔΔETS^d	ΔΔG^e	ΔΔE^f	τ99.9%^g
a The Gibbs free energy of the product relative to the reactant of the tautomerisation reaction (T = 298.15 K), kcal mol^−1.b The electronic energy of the product relative to the reactant of the tautomerisation reaction, kcal mol^−1.c The Gibbs free energy barrier for the forward reaction of tautomerisation, kcal mol^−1.d The electronic energy barrier for the forward reaction of tautomerisation, kcal mol^−1.e The Gibbs free energy barrier for the reverse reaction of tautomerisation, kcal mol^−1.f The electronic energy barrier for the reverse reaction of tautomerisation, kcal mol^−1.g The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerisation reaction, s.h See also summary Table S1 for the Gibbs and electronic energies of the mispairs and TSs relative to the global minimum – the long Watson–Crick-like A·G(WC) DNA base mispair.
A·G(WC) ↔ A·G*↓(w)
MP2/6-311++G(2df,pd)	3.27	5.70	16.88	16.94	13.60	11.24	9.71 × 10^−3
MP2/6-311++G(3df,2pd)	3.63	6.06	16.79	16.86	13.16	10.79	4.60 × 10^−3
MP2/cc-pVTZ	3.88	6.31	17.73	17.79	13.84	11.48	1.45 × 10^−2
MP2/cc-pVQZ	3.76	6.19	17.01	17.07	13.25	10.88	5.31 × 10^−3
A·G(WC) ↔ A·G*↑(w)
MP2/6-311++G(2df,pd)	6.14	7.34	25.48	25.37	19.34	18.03	1.52 × 10^2
MP2/6-311++G(3df,2pd)	6.36	7.56	25.97	25.86	19.61	18.29	2.37 × 10^2
MP2/cc-pVTZ	6.34	7.54	25.35	25.23	19.01	17.69	1.15 × 10^2
MP2/cc-pVQZ	6.28	7.48	25.79	25.68	19.51	18.20	2.02 × 10^2
A·G(WC) ↔ A*·G↑(w)
MP2/6-311++G(2df,pd)	14.16	13.96	24.95	24.05	10.79	10.09	8.45 × 10^−5
MP2/6-311++G(3df,2pd)	14.11	13.91	25.01	24.11	10.90	10.20	1.02 × 10^−4
MP2/cc-pVTZ	14.03	13.83	25.46	24.56	11.43	10.73	2.49 × 10^−4
MP2/cc-pVQZ	14.29	14.09	25.29	24.39	11.00	10.30	1.21 × 10^−4
A·G(WC) ↔ A*·G↓(w)
MP2/6-311++G(2df,pd)	21.01	22.54	49.23	49.70	28.22	27.16	4.66 × 10^8
MP2/6-311++G(3df,2pd)	20.73	22.26	48.94	49.41	28.21	27.15	4.57 × 10^8
MP2/cc-pVTZ	21.39	22.92	49.53	50.00	28.14	27.08	4.05 × 10^8
MP2/cc-pVQZ	21.11	22.65	49.20	49.67	28.08	27.02	3.67 × 10^8

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The A·G(WC) ↔ A·G*_↓(w) and A·G(WC) ↔ A*·G_↑(w) tautomerisation reactions are accompanied by the substantial rebuilding of the A·G(WC) DNA base mispair from Watson–Crick to wobble sizes and vice versa; that is displayed by the significant changes in its glycosidic parameters, namely the R(H₉–H_9′) glycosidic distances and the α₁ and α₂ glycosidic angles, varying largely without ruptures (Fig. S1†). Both transition states of these reactions represent themselves as highly polar and highly stable A⁺·G⁻ tight ion pairs shifted towards minor or major DNA grooves, respectively.

Also, we have obtained 11 unique patterns of the specific intermolecular interactions, including AH⋯B H-bonds and loosened A–H–B covalent bridges consistently replacing each other, together with van der Waals contact, during these tautomerisation processes (Fig. 3 and Table 3). Two loosened A–H–B covalent bridges that are linked with H-bonds display the common feature of these transformations. Notably, in the case of the A·G(WC) ↔ A·G*_↓(w) pathway, the N6H⋯O6 H-bond continuously exists along the whole IRC. The N2H⋯HC2 DH-bond^11,52 smoothly and without bifurcations transforms into the C2H⋯N2 H-bond in the course of the A·G(WC) ↔ A·G*_↓(w) tautomerisation. The formation of the attractive N6⋯N2 van der Waals contact precedes the appearance of the N2H⋯N6 H-bond during the A·G(WC) ↔ A*·G_↑(w) route. It has been established that the base pair that tautomerises remains in the A⁺·G⁻ highly polar state, stabilized by rather strong electrostatic interactions, in a wide range of the IRC (−13.94 to 4.17 and −13.21 to 7.13 Bohr for the A·G(WC) ↔ A·G*_↓(w) and A·G(WC) ↔ A*·G_↑(w) conversions, respectively) (Fig. 3 and Tables 3 and S2†).

Fig. 3 Exchange of the patterns of the intermolecular AH⋯B H-bonds (their energies, E_AH⋯B, are estimated by the EML formula at the (3,−1) BCPs) along the IRC of the (a) A·G(WC) ↔ A·G*_↓(w) and (b) A·G(WC) ↔ A*·G_↑(w) biologically important tautomerisations via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory (see Tables 1 and 3).

Table 3 Patterns of the intermolecular interactions, including AH⋯B H-bonds and loosened A–H–B covalent bridges, that sequentially replace each other, along the IRC of the A·G(WC) ↔ A·G*_↓(w) and A·G(WC) ↔ A*·G_↑(w) biologically important tautomerisations via the sequential DPT and their ranges of existence, obtained at the B3LYP/6-311++G(d,p) level of theory (see Fig. 1–3)

Patterns	IRC range, Bohr	Intermolecular interactions, forming patterns
A·G(WC) ↔ A·G*↓(w)
I	[−28.96 to −21.06)	(A)N6H⋯O6(G), (G)N1H⋯N1(A), (G)N2H⋯HC2(A)
II	[−21.06 to −14.44)	(A)N6H⋯O6(G), (G)N1H⋯N1(A), (A)C2H⋯N2(G)
III	[−14.44 to −13.94)	(G)N1–H–N1(A), (A)N6H⋯O6(G), (A)C2H⋯N2(G)
IV	[−13.94 to −3.39)	(A)N6H⋯O6(G), (A)N1H⋯N1(G), (A)C2H⋯N2(G)
V	[−3.39 to −2.74)	(A)N6H⋯O6(G), (A)N1H⋯N1(G)
VI	[−2.74 to 1.17)	(A)N6H⋯O6(G), (A)N1H⋯N1(G), (A)N1H⋯O6(G)
VII	[1.17–3.39)	(A)N6H⋯O6(G), (A)N1H⋯O6(G)
VIII	[3.39–4.17)	(A)N6H⋯O6(G), (A)N1H⋯O6(G), (A)C2H⋯N2(G)
IX	[4.17–4.69)	(A)N1–H–O6(G), (A)N6H⋯O6(G), (A)C2H⋯N2(G)
X	[4.69–17.54)	(G)O6H⋯N1(A), (A)N6H⋯O6(G), (A)C2H⋯N2(G)
XI	[17.54–20.80]	(G)O6H⋯N1(A), (A)N6H⋯O6(G)
A·G(WC) ↔ A*·G↑(w)
I	[−24.61 to −13.75)	(A)N6H⋯O6(G), (G)N1H⋯N1(A), (G)N2H⋯HC2(A)
II	[−13.75 to −13.21)	(G)N1–H–N1(A), (A)N6H⋯O6(G), (G)N2H⋯HC2(A)
III	[−13.21 to −5.96)	(A)N6H⋯O6(G), (A)N1H⋯N1(G), (G)N2H⋯HC2(A)
IV	[−5.96 to −4.50)	(A)N6H⋯O6(G), (A)N1H⋯N1(G)
V	[−4.50 to −3.04)	(A)N6H⋯O6(G), (A)N1H⋯N1(G), (A)N1H⋯N2(G)
VI	[−3.04 to 0.45)	(A)N6H⋯O6(G), (A)N6H⋯N1(G), (A)N1H⋯N1(G), (A)N1H⋯N2(G)
VII	[0.45–7.13)	(A)N6H⋯N1(G), (A)N1H⋯N2(G)
VIII	[7.13–7.55)	(A)N6–H–N1(G), (A)N1H⋯N2(G)
IX	[7.55–17.80)	(G)N1H⋯N6(A), (A)N1H⋯N2(G)
X	[17.80–19.25)	(G)N1H⋯N6(A), (A)N1H⋯N2(G), (A)N6⋯N2(G)
XI	[19.25–28.57]	(G)N1H⋯N6(A), (A)N1H⋯N2(G), (G)N2H⋯N6(A)

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It is known that one of the necessary conditions for the successful incorporation of the incorrect DNA base pair into the structure of the DNA double helix is its flatness or (in the case of a non-planar structure) the ability to adapt its geometry to a planar configuration.^57,67,68

To ensure that the considered DNA base mispairs and transition states of their mutagenic tautomerisation with non-planar structures are involved in the biologically important processes of tautomerisation through the sequential DPT – namely, A·G(WC), A*·G_↑(w), TS^A+·G−_{A·G(WC)↔A*·G↑(w)} and TS^A+·G−_{A·G(WC)↔A·G*↓(w)} – we investigated their structural non-rigidity, i.e. the ability of their mirror-symmetric conformers to mutually transform (interconvert) into each other.

It has been found in all cases that the transition states of their interconversion are plane-symmetric structures, while in the case of the Watson–Crick-like A·G(WC) base mispair and TS^A+·G−_{A·G(WC)↔A·G*↓(w)}, they are plane complexes (Fig. S2 and S3 and Table S3†). This interconversion of the mirror-symmetric conformers of the slightly non-planar A·G(WC) base mispair and the TS^A+·G−_{A·G(WC)↔A·G*↓(w)} transition state is realized by the mechanism of the planar inversion of the amino fragment of the G base. In all other cases the mechanism of the interconversion is reduced to the rotation of the amino group of the G base via the plane symmetric transition state, when its amine nitrogen atom N2 acts as a donor for the H-bonding (Fig. S2 and S3†). It is characteristic that these processes occur without dissociation of the complexes into the monomers. For all investigated structures, their energy of planarization, ΔΔG_TS, is considerably less than the energy of the stacking interactions of the neighboring DNA base pairs,⁵⁷ and these processes are quite fast (τ_99.9% = 1.6 × 10⁻¹¹ to 1.2 × 10⁻⁷ s) (Table S3†). This gives us a reason to believe that all of the studied structures have every chance to be integrated into the structure of the DNA double helix.

2. Mutagenic tautomerisation of the short C·T Watson–Crick DNA base mispair

As in the case of the A·G(WC) mispair, the tautomerisation process of the C·T(WC) DNA base mispair into the wobble mismatches is also accompanied by the individual transitions of the C and T bases in its composition into the C* and T* mutagenic tautomeric forms, respectively. As a result of this, four different H-linked wobble C*·T_↓(w), C*·T_↑(w), C·T*_↓(w) and C·T*_↑(w) DNA base pairs are formed (Fig. 4 and 5). The C·T(WC) ↔ C*·T_↑(w) and C·T(WC) ↔ C·T*_↓(w) tautomerisation processes are much faster than the slow C·T(WC) ↔ C*·T_↓(w) and C·T(WC) ↔ C·T*_↑(w) transitions (Tables 4 and 5), that make no biological sense due to the reasons outlined above for the conversion of the A·G(WC) nucleobase mispair.

Fig. 4 Structures corresponding to the stationary points on the reaction pathways of the (a) C·T(WC) ↔ C*·T*(WC), (b) C*·T*(WC) ↔ C*·T_↑(w), (c) C*·T*(WC) ↔ C·T*_↓(w), (d) C·T(WC) ↔ C*·T_↓(w) and (e) C·T(WC) ↔ C·T*_↑(w) conversions via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory. The dotted lines indicate AH⋯B H-bonds and attractive A⋯B van der Waals contacts (their lengths are presented in angstroms). Carbon atoms are in light-blue, nitrogen in dark-blue, hydrogen in grey and oxygen in red. ν_i = imaginary frequency.

Fig. 5 Profiles of the relative electronic energy, ΔE, of the DNA base mispairs along the IRC of the (a) C·T(WC) ↔ C*·T_↑(w), (b) C·T(WC) ↔ C·T*_↓(w), (c) C·T(WC) ↔ C*·T_↓(w) and (d) C·T(WC) ↔ C·T*_↑(w) tautomerisations via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory.

Table 4 Electron-topological, structural, vibrational and energetic characteristics of the intermolecular H-bonds and attractive vdW contacts revealed in the DNA base mispairs containing C and T nucleobases and TSs of their mutual transformations via the sequential DPT and structural displacement of the C and T bases relative to each other, the energetic and polar characteristics of the latter are obtained at the B3LYP/6-311++G(d,p) level of theory^l

Base pair/TS	AH⋯B H-bond/A⋯B vdW contact	ρ^a	Δρ^b	100ε^c	dA⋯B^d	dH⋯B^e	ΔdAH^f	∠AH⋯B^g	Δν^h	EAH⋯B/O⋯O/N^i	ΔG^j	μ^k
a The electron density at the (3,−1) BCP of the H-bond, a.u.b The Laplacian of the electron density at the (3,−1) BCP of the H-bond, a.u.c The ellipticity at the (3,−1) BCP of the H-bond.d The distance between the A (H-bond donor) and B (H-bond acceptor) atoms of the AH⋯B H-bond, Å.e The distance between the H and B atoms of the AH⋯B H-bond, Å.f The elongation of the H-bond donating group AH upon AH⋯B H-bonding, Å.g The H-bond angle, degree.h The redshift of the stretching vibrational mode ν(AH) of the AH H-bonded group, cm^−1.i Energy of the H-bonds, calculated by Iogansen’s,^56 Espinosa–Molins–Lecomte (marked with an asterisk)^53,54 and Nikolaienko–Bulavin–Hovorun (denoted by double asterisk)^55 formulas, kcal mol^−1.j The relative Gibbs free energy of the complex obtained at the MP2/cc-pVQZ//B3LYP/6-311++G(d,p) level of theory under normal conditions, kcal mol^−1.k The dipole moment of the complex, D.l Data are taken from the literature.^12
C·T(WC)^l	N4H⋯O4	0.031	0.108	3.48	2.873	1.851	0.016	174.8	287.3	5.19	0.00	4.05
	N3H⋯N3	0.028	0.078	6.50	3.001	1.974	0.024	170.1	408.2	6.33
	O2⋯O2	0.002	0.008	21.46	3.730	—	—	—	—	0.32*
C*·T↑(w)	N3H⋯N4	0.039	0.095	6.30	2.877	1.838	0.032	172.4	549.4	7.45	0.52	1.08
	N3H⋯O2	0.028	0.100	4.31	2.906	1.882	0.017	173.0	282.1	5.13
C*·T↓(w)	N3H⋯O4	0.027	0.097	2.86	2.912	1.902	0.016	166.8	255.1	4.84	3.08	0.54
	N3H⋯O2	0.029	0.106	3.75	2.878	1.860	0.017	169.6	277.0	5.08
C·T*O2(w)	N4H⋯N3	0.038	0.097	7.66	2.874	1.849	0.027	170.5	485.6	6.97	6.25	2.06
	O2H⋯N3	0.059	0.093	5.52	2.684	1.659	0.058	175.8	1088.0	10.68
TSC*·T↑(w)↔C·T*O2(w)	N4H⋯N3	0.060	0.097	6.07	2.728	1.666	—	172.6	—	11.49**	6.67	5.08
C*·T*(WC)^l	O4H⋯N4	0.066	0.096	4.69	2.637	1.611	0.060	173.9	1129.2	10.89	9.13	3.98
	N3H⋯N3	0.029	0.081	6.32	2.974	1.959	0.024	165.9	409.7	6.34
	O2⋯O2	0.002	0.008	26.46	3.744	—	—	—	—	0.30*
TSC·T(WC)↔C*·T*(WC)^l	N3H⋯N3	0.052	0.092	5.95	2.781	1.728	—	167.6	—	9.67**	9.53	5.86
	O2⋯O2	0.002	0.009	17.67	3.639	—	—	—	—	0.41*
C·T*↓(w)	N4H⋯O4	0.012	0.042	23.47	3.120	2.312	0.003	136.2	49.2	1.00	12.05	7.36
	O4H⋯N3	0.045	0.099	3.29	2.727	1.774	0.034	157.2	651.6	8.16
C·T*↑(w)	O4H⋯N4	0.026	0.074	6.84	2.966	2.002	0.013	166.3	266.8	4.97	15.69	7.10
	N4H⋯N3	0.015	0.050	17.23	3.032	2.316	0.010	126.4	143.1	3.35
TS^C+·T−C*·T*(WC)↔C*·T↑(w)	N4^+H⋯O4^−	0.032	0.097	5.23	2.821	1.866	0.033	150.5	523.7	4.33	17.03	8.32
	N4^+H⋯N3^−	0.024	0.081	30.73	2.913	2.040	0.033	139.4	523.7	2.93
	N3^+H⋯N3^−	0.020	0.064	15.00	3.014	2.138	0.027	140.1	421.0	3.19
	N3^+H⋯O2^−	0.020	0.061	14.61	3.054	2.078	0.027	154.8	421.0	3.25
TS^C+·T−C*·T*(WC)↔C·T*↓(w)	N4^+H⋯O4^−	0.062	0.174	5.42	2.538	1.558	0.049	151.2	793.2	9.06	26.62	12.16
	N3^+H⋯O4^−	0.036	0.105	5.12	2.731	1.840	0.036	140.1	559.9	7.52
TS^C−·T+C·T(WC)↔C*·T↓(w)	O4^+H⋯N4^−	0.037	0.082	3.70	2.765	1.837	0.059	148.3	957.5	5.82	34.39	5.92
	O4^+H⋯N3^−	0.027	0.079	27.99	2.848	1.982	0.059	140.1	957.5	4.18
	N3^+H⋯N3^−	0.018	0.067	131.66	2.977	2.175	0.039	131.1	618.5	2.55
	N3^+H⋯O2^−	0.035	0.094	0.92	2.854	1.835	0.039	161.1	618.5	5.38
TS^C−·T+C·T(WC)↔C·T*↑(w)	O4^+H⋯N4^−	0.054	0.107	6.50	2.615	1.678	0.051	150.7	940.9	9.90	46.74	10.54
	N3^+H⋯N4^−	0.086	0.046	5.77	2.617	1.531	0.136	154.3	1541.6	12.79
	O2^+⋯N3^−	0.003	0.010	118.00	3.684	—	—	—	—	0.48*

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Table 5 Energetic and kinetic characteristics of the C·T(WC) ↔ C*·T*(w), C*·T*(WC) ↔ C*·T_↑(w), C*·T*(WC) ↔ C·T*_↓(w), C·T(WC) ↔ C*·T_↓(w) and C·T(WC) ↔ C·T*_↑(w) tautomerisations via the sequential DPT of the C and T bases obtained at different levels of theory for the geometry calculated at the B3LYP/6-311++G(d,p) level of theory (see also Fig. 4 and Table S1)^h

Level of theory	ΔG^a	ΔE^b	ΔΔGTS^c	ΔΔETS^d	ΔΔG^e	ΔΔE^f	τ99.9%^g
a The Gibbs free energy of the product relative to the reactant of the tautomerisation reaction (T = 298.15 K), kcal mol^−1.b The electronic energy of the product relative to the reactant of the tautomerisation reaction, kcal mol^−1.c The Gibbs free energy barrier for the forward reaction of tautomerisation, kcal mol^−1.d The electronic energy barrier for the forward reaction of tautomerisation, kcal mol^−1.e The Gibbs free energy barrier for the reverse reaction of tautomerisation, kcal mol^−1.f The electronic energy barrier for the reverse reaction of tautomerisation, kcal mol^−1.g The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerisation reaction, s.h See also summary Table S1 for the Gibbs and electronic energies of the mispairs and TSs relative to the global minimum – the short C·T(WC) Watson–Crick DNA base mispair.i Data are taken from the literature.^12
C·T(WC) ↔ C*·T*(WC)^i
MP2/6-311++G(2df,pd)	8.97	8.81	9.08	10.91	0.11	2.10	1.31 × 10^−13
MP2/6-311++G(3df,2pd)	9.24	9.08	9.54	11.37	0.30	2.29	1.84 × 10^−13
MP2/cc-pVTZ	8.82	8.66	9.36	11.19	0.54	2.53	2.70 × 10^−13
MP2/cc-pVQZ	9.15	8.99	9.55	11.38	0.40	2.39	2.13 × 10^−13
C*·T*(WC) ↔ C*·T↑(w)
MP2/6-311++G(2df,pd)	−8.31	−8.17	8.38	17.02	16.69	25.18	1.52 × 10^−6
MP2/6-311++G(3df,2pd)	−8.68	−8.54	7.88	8.35	16.56	16.89	6.61 × 10^−7
MP2/cc-pVTZ	−8.40	−8.25	8.54	9.01	16.94	17.27	2.01 × 10^−6
MP2/cc-pVQZ	−8.59	−8.44	7.90	8.37	16.48	16.81	6.76 × 10^−7
C*·T*(WC) ↔ C·T*↓(w)
MP2/6-311++G(2df,pd)	2.87	5.53	17.74	16.58	14.87	11.05	8.89 × 10^−2
MP2/6-311++G(3df,2pd)	2.86	5.53	17.44	16.28	14.57	10.75	5.39 × 10^−2
MP2/cc-pVTZ	3.23	5.90	18.32	17.17	15.09	11.27	1.30 × 10^−1
MP2/cc-pVQZ	2.92	5.58	17.49	16.33	14.57	10.75	5.38 × 10^−2
C·T(WC) ↔ C*·T↓(w)
MP2/6-311++G(2df,pd)	3.31	3.42	34.41	35.70	31.10	32.28	6.49 × 10^10
MP2/6-311++G(3df,2pd)	2.97	3.09	34.23	35.52	31.26	32.43	8.45 × 10^10
MP2/cc-pVTZ	3.09	3.20	34.66	35.95	31.57	32.75	1.44 × 10^11
MP2/cc-pVQZ	3.10	3.22	34.40	35.70	31.30	32.48	9.09 × 10^10
C·T(WC) ↔ C·T*↑(w)
MP2/6-311++G(2df,pd)	15.60	16.97	46.51	47.72	30.91	30.75	3.52 × 10^10
MP2/6-311++G(3df,2pd)	15.88	17.26	46.87	48.08	30.99	30.83	4.00 × 10^10
MP2/cc-pVTZ	15.64	17.02	46.66	47.87	31.01	30.86	4.20 × 10^10
MP2/cc-pVQZ	15.70	17.07	46.76	47.97	31.06	30.90	4.55 × 10^10

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It is interesting to note that the TS^C−·T+_{C·T(WC)↔C·T*↑(w)} transition state is stabilized, except for two O4⁺H⋯N4⁻ (9.90) and N3⁺H⋯N4⁻ (12.79) H-bonds, which are locked on the one and the same N4⁻ nitrogen atom by the attractive N3⁺⋯O2⁻ (0.48 kcal mol⁻¹) van der Waals contact (Table 4).

Both of the biologically important C·T(WC) ↔ C*·T_↑(w) and C·T(WC) ↔ C·T*_↓(w) tautomerisation processes are at first initiated by the very fast (τ_99.9% = 2.13 × 10⁻¹³ s) C·T(WC) → C*·T*(WC) double proton transfer along intermolecular H-bonds that was previously investigated in detail,¹² followed by the formation of the C*·T*(WC) base pair, that in both cases is a dynamically unstable intermediate (Table 5). The highly polar TS^C+·T−_{C*·T*(WC)↔C*·T↑(w)} and TS^C+·T−_{C*·T*(WC)↔C·T*↓(w)} transition states, that are stabilized in addition to the strong electrostatic interactions by the four N4⁺H⋯O4⁻ (4.33), N4⁺H⋯N3⁻ (2.93), N3⁺H⋯N3⁻ (3.19), N3⁺H⋯O2⁻ (3.25) and two N4⁺H⋯O4⁻ (9.06), N3⁺H⋯O4⁻ (7.52 kcal mol⁻¹) H-bonds, respectively, are created by the displacement of the deprotonated T⁻ base relative to the protonated C⁺ base towards the major and minor DNA grooves, correspondingly. Each of the terminal structures – the tautomerised C*·T_↑(w) (∠C4N3(C*)C2N3(T) = 0.0°) and C·T*_↓(w) (∠C4N3(C)C2N3(T*) = 34.3°) pairs with wobble geometry involving the C* and T* mutagenic tautomers – are stabilized by two intermolecular N3H⋯N4 (7.45), N3H⋯O2 (5.13) and N4H⋯O4 (1.00), O4H⋯N3 (8.16 kcal mol⁻¹) H-bonds, respectively.

Both the TS^C+·T−_{C*·T*(WC)↔C·T*↓(w)} transition state and the tautomerised C·T*_↓(w) DNA base pair, involved in the biologically important process of the C·T(WC) ↔ C·T*_↓(w) mutagenic tautomerisation, are united by two intermolecular H-bonds. In the first case, the O4⁻ oxygen atom of the T⁻ base is a joint acceptor of the N4⁺H⋯O4⁻ (9.06) and N3⁺H⋯O4⁻ (7.52 kcal mol⁻¹) H-bonds. In the latter case, the O4H hydroxyl group of the T* base acts simultaneously as a donor and an acceptor for the H-bonding – N4H⋯O4 (1.00) and O4H⋯N3 (8.16 kcal mol⁻¹) (Table 4).

In fact, the DPT tautomerisation of the biologically important C*·T_↑(w) nucleobase mispair into the C·T*_O2↑(w) mismatch (Fig. S4 and S5 and Table S4†) does not occur, since the last mispair is a dynamically unstable structure and any of its six intermolecular vibrations (21.7, 29.3, 59.8, 77.0, 95.3 and 102.9 cm⁻¹) can develop during its lifetime (τ = 2.06 × 10⁻¹³ s). The planar C·T*_↓(w) nucleobase mispair can be successfully incorporated into the structure of the DNA double helix, since the energy of its planarization (ΔΔG_TS = 4.69 kcal mol⁻¹ under normal conditions (Table S3†)) is noticeably smaller than the energy of the stacking interactions between the Watson–Crick DNA base pairs.⁵⁷

Both of the C·T(WC) → C*·T_↑(w) and C·T(WC) → C·T*_↓(w) tautomerisation reactions, that are able to cause the C* and T* mutagenic tautomers, occur by the non-dissociative mechanism. This fact can be easily confirmed by the inseparable character of the profiles of the R(H₁–H_1′) glycosidic distances and the α₁ and α₂ glycosidic angles (Fig. S6†).

Another distinguishing feature of these tautomeric conversions is their accompaniment of the unique patterns of the changing intermolecular interactions: there are 14 specific contacts, including 2 to 4 H-bonds and a single attractive van der Waals contact, for the C·T(WC) ↔ C*·T_↑(w) process and 12 specific contacts, among which there are a maximum of 2 H-bonds and a single attractive van der Waals contact, for the C·T(WC) ↔ C·T*_↓(w) process. A common feature of these sweeps is the sequential interchange between the N4H⋯O4 and O4H⋯N4 H-bonds, with their respective formation and disruption occurring via the N4–H–O4 loosened covalent bridge (Fig. 6 and Table 6). The simultaneous existence of the N4H⋯O4/N3 and N3H⋯N3/O2 H-bonds within IRC = 13.71–42.02 Bohr and the N4H⋯O4 and N3H⋯O4 H-bonds within IRC = 14.70–42.02 Bohr for the C·T(WC) ↔ C*·T_↑(w) and C·T(WC) ↔ C·T*_↓(w) tautomerisation reactions, accordingly, reflects the existence of the highly polar C⁺·T⁻ tight ion pair (Table 6).

Fig. 6 Exchange of the patterns of the intermolecular AH⋯B H-bonds and attractive O⋯O vdW contacts (their energies, E_AH⋯B/O⋯O, are estimated by the EML formula at the (3,−1) BCPs) along the IRC of the (a) C·T(WC) ↔ C*·T_↑(w) and (b) C·T(WC) ↔ C·T*_↓(w) biologically important tautomerisations via the sequential DPT, obtained at the B3LYP/6-311++G(d,p) level of theory (see Tables 4 and 6).

Table 6 Patterns of the intermolecular interactions, including AH⋯B H-bonds, attractive O⋯O vdW contacts and loosened A–H–B covalent bridges that sequentially replace each other, along the IRC of the C·T(WC) ↔ C*·T_↑(w) and C·T(WC) ↔ C·T*_↓(w) biologically important tautomerisations via the sequential DPT and their ranges of existence, obtained at the B3LYP/6-311++G(d,p) level of theory (see Fig. 4–6)

Patterns	IRC range, Bohr	Intermolecular interactions, forming patterns
C·T(WC) ↔ C*·T↑(w)
I	[−9.30 to −3.55)	(C)N4H⋯O4(T), (T)N3H⋯N3(C), (C)O2⋯O2(T)
II	[−3.55 to −3.12)	(C)N4H⋯O4(T), (T)N3–H–N3(C), (C)O2⋯O2(T)
III	[−3.12 to −0.05)	(C)N4H⋯O4(T), (C)N3H⋯N3(T), (C)O2⋯O2(T)
IV	[−0.05 to 0.32)	(C)N4–H–O4(T), (C)N3H⋯N3(T), (C)O2⋯O2(T)
V	[0.32–8.32)	(T)O4H⋯N4(C), (C)N3H⋯N3(T), (C)O2⋯O2(T)
VI	[8.32–13.71)	(T)O4–H–N4(C), (C)N3H⋯N3(T), (C)O2⋯O2(T)
VII	[13.71–14.70)	(C)N4H⋯O4(T), (C)N3H⋯N3(T), (C)O2⋯O2(T)
VIII	[14.70–19.47)	(C)N4H⋯O4(T), (C)N3H⋯N3(T), (C)N3H⋯O2(T), (C)O2⋯O2(T)
IX	[19.47–23.29)	(C)N4H⋯O4(T), (C)N4H⋯N3(T), (C)N3H⋯N3(T), (C)N3H⋯O2(T), (C)O2⋯O2(T)
X	[23.29–42.02)	(C)N4H⋯O4(T), (C)N4H⋯N3(T), (C)N3H⋯N3(T), (C)N3H⋯O2(T)
XI	[42.02–42.44)	(C)N4H⋯O4(T), (C)N4H⋯N3(T), (C)N3H⋯O2(T)
XII	[23.29–42.02)	(C)N4H⋯N3(T), (C)N3H⋯O2(T)
XIII	[42.02–42.44)	(C)N4–H–N3(T), (C)N3H⋯O2(T)
XIV	[42.44–48.95]	(T)N3H⋯N4(C), (C)N3H⋯O2(T)
C·T(WC) ↔ C·T*↓(w)
I	[−9.30 to −3.55)	(C)N4H⋯O4(T), (T)N3H⋯N3(C), (C)O2⋯O2(T)
II	[−3.55 to −3.12)	(C)N4H⋯O4(T), (T)N3–H–N3(C), (C)O2⋯O2(T)
III	[−3.12 to −0.05)	(C)N4H⋯O4(T), (C)N3H⋯N3(T), (C)O2⋯O2(T)
IV	[−0.05 to 0.32)	(C)N4–H–O4(T), (C)N3H⋯N3(T), (C)O2⋯O2(T)
V	[0.32–8.32)	(T)O4H⋯N4(C), (C)N3H⋯N3(T), (C)O2⋯O2(T)
VI	[8.32–13.71)	(T)O4H⋯N4(C), (C)N3H⋯N3(T)
VII	[13.71–14.70)	(T)O4–H–N4(C), (C)N3H⋯N3(T)
VIII	[14.70–19.47)	(C)N4H⋯O4(T), (C)N3H⋯N3(T)
IX	[19.47–23.29)	(C)N4H⋯O4(T), (C)N3H⋯O4(T), (C)N3H⋯N3(T)
X	[23.29–42.02)	(C)N4H⋯O4(T), (C)N3H⋯O4(T)
XI	[42.02–42.44)	(C)N4H⋯O4(T), (C)N3–H–O4(T)
XII	[42.44–48.95]	(C)N4H⋯O4(T), (T)O4H⋯N3(C)

---

3. Biological implication of the revealed routes of the mutagenic tautomerisation of the A·G and C·T DNA base mispairs with a Watson–Crick shape

The starting point of the study (now there are already all grounds to consider it as universal in the field of spontaneous point mutagenesis) is the classical Watson–Crick tautomeric hypothesis, which now is already partially implemented at the level of “molecular phenomenology”.^1,3,69,70

It is characteristic that for all four biologically important, thermodynamically stable tautomerised A·G*_↓(w), A*·G_↑(w) and C*·T_↑(w), C·T*_↓(w) DNA base mispairs, their lifetime, τ, is by many orders greater than the time (several nanoseconds⁷¹) necessary for the DNA-polymerase to cause the forced dissociation of the pairs during DNA replication. Moreover, the energy of the interaction between the bases within these pairs is less (Table S2†) than the analogical value for the G·C Watson–Crick DNA base pair (29.28 kcal mol⁻¹ (ref. 14)). These two facts together mean that DNA-polymerase is able to successfully dissociate all these mispairs, with the participation of the mutagenic tautomers, into the monomers without changing their tautomeric status. In such a way, the A·G(WC) → A·G*_↓(w), A·G(WC) → A*·G_↑(w), C·T(WC) → C*·T_↑(w) and C·T(WC) → C·T*_↓(w) tautomerisation processes may be responsible for the generation of the mutagenic tautomers of the canonical DNA bases during DNA replication and are perfectly acceptable alternatives for the classical Löwdin mechanism.^19,20

Moreover, the results obtained in this paper allow us to understand, at least at the semi-quantitative level, in what way the A·G/G·A and C·T/T·C non-equivalent¹⁸ errors are formed during DNA replication within the framework of the classical tautomeric hypothesis. It turns out that the mutagenic tautomer of each DNA base (A*, G*, C* and T*) belonging to the template can interact not only with the C, T, A and G DNA bases, accordingly, as it was previously thought,^1,3,69,70 but also with the G, A, T and C bases, respectively, forming the aforementioned wobble A·G*_↓(w), A*·G_↑(w), C*·T_↑(w) and C·T*_↓(w) pairs with all the consequences arising therefrom.

All the shifted thermodynamically stable (ΔG_int < 0 (Table S2†)) C*·T_↑(w), C·T*_↓(w) and A·G*_↓(w), A*·G_↑(w) DNA base mispairs may acquire an enzymatically competent conformation, tautomerising directly into the short Watson–Crick-like C·T(WC) base pair or through the A·G(WC)/G·A(WC) intermediates into the G·A_syn and A*·G*_syn pairs,⁷² respectively.

Conclusions

A novel mechanism for the mutagenic tautomerisation of the long A·G(WC) and short C·T(WC) Watson–Crick DNA base pairs was uncovered for the first time. The tautomerisation of each mispair proceeds via four topologically and energetically different ways through highly stable transition states – H-bonded tight ion pairs, comprising protonated and deprotonated bases.

The non-dissociative tautomerisation process is accompanied by the significant changing of the binding architecture from the Watson–Crick to the wobble geometry, both towards the minor, as well as the major DNA grooves and vice versa. In all cases, the tautomerisation reactions are concerted and stepwise.

It was established for the first time that the fast, biologically important processes of the mutagenic tautomerisation of the A·G(WC) and C·T(WC) base pairs are initiated by the transition of the more acidic imino protons and are determined by the transition states of the A⁺·G⁻ and C⁺·T⁻ tight ion pair type. On the contrary, the moving of the less acidic amino proton with the formation of the transition states of the A⁻·G⁺ and C⁻·T⁺ types causes a too slow mutagenic tautomerisation that has no real biological meaning.

The biological significance of the obtained results is twofold. First, it has been discovered for the first time that the phenomenon of tautomerisation can be the source of the mutagenic tautomers of all four canonical nucleobases at DNA replication, since the wobble A·G*_↓(w), A*·G_↑(w), C*·T_↑(w) and C·T*_↓(w) tautomerised pairs meet all necessary requirements for this to occur.⁷¹

Second, these results allow us to understand the basic physico-chemical principles of the arising of some DNA replication errors caused by the random mutagenic tautomerisation of the nucleotide bases belonging to the template. It becomes clear in what way the wobble C*·T(w), T*·C(w), A*·G(w) and G*·A(w) pairs (base belonging to the incoming nucleotide is placed on the right) transform, either into the short C·T(WC) and T·C(WC) Watson–Crick base pairs, or into the long A·G(WC) and G·A(WC) Watson–Crick base pairs. This knowledge is important, since high-fidelity DNA-polymerase selects base mispairs based on their ability to acquire a Watson–Crick-like configuration in its active site in the closed conformation state during the catalytic cycle.^73–77 The process of the acquisition of the enzymatically competent conformation in the hydrophobic recognition pocket of the high-fidelity DNA-polymerase has been earlier described by us in detail.⁷⁸

Overall, elucidation of the novel mechanisms of the tautomerisation of DNA bases eventually gives a theoretical background for the experimental observations,^73–77 allowing us to suppose that DNA-polymerase is able to make errors due to the formation of the rare tautomers, incorporated into the structure of the wrong mispairs, mimicking the shape of the canonical Watson–Crick pairs.⁷⁹ So, ultimately these mismatches can be accommodated without obstacles into the structure of the DNA double helix.

Acknowledgements

O. O. B. was supported by the grant of the President of Ukraine to support the scientific research of young scientists for the year 2015 from the State Fund for Fundamental Research of Ukraine (project No. GP/F61/028), and by the grant of the National Academy of Sciences of Ukraine for the scientific and research work of young scientists for the years 2015–2016 and by the Scholarship of the President of Ukraine for young scientists for the years 2014–2016. This work was performed using the computational facilities of the joint computer cluster of SSI “Institute for Single Crystals” of the National Academy of Sciences of Ukraine and the Institute for Scintillation Materials of the National Academy of Sciences of Ukraine incorporated into the Ukrainian National Grid. The authors sincerely thank Dr Ivan S. Voiteshenko (Institute of High Technologies, Taras Shevchenko National University of Kyiv) and Dr Fernando R. Clemente (Gaussian, Inc.) for their technical assistance of the work.

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Footnote

† Electronic supplementary information (ESI) available: (i) Energetic characteristics of the investigated DNA mispairs; (ii) profiles of the glycosidic parameters along the IRC of tautomerisation; (iii) energetic profiles and parameters of the mismatch planarization. See DOI: 10.1039/c5ra11773a

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