Physico-chemical profiles of the wobble ↔ Watson–Crick G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) tautomerisations: a QM/QTAIM comprehensive survey

Abstract

This study is intended to clarify in detail the tautomeric transformations of the wobble (w) G*·2AP(w) and A·2AP(w) nucleobase mispairs involving 2-aminopurine (2AP) into the Watson–Crick (WC) G·2AP(WC) and A*·2AP(WC) base mispairs (asterisks denote mutagenic tautomers of the DNA bases), respectively, by quantum-mechanical methods and Bader's Quantum Theory of Atoms in Molecules. Our previously reported methodology has been used, which allows the evolution of the physico-chemical parameters to be tracked along the entire internal reaction coordinate (IRC), not exclusively in the stationary states of these reactions. These biologically important G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations, which are involved in mutagenic tautomerically-conformational pathways, determine the origin of the transitions and transversions induced by 2AP. In addition, it is established that they proceed through planar, highly stable, zwitterionic transition states and they exhibit similar physico-chemical profiles and stages of sequential intrapair proton transfer, followed by spatial rearrangement of the nucleobases relative to each other within the base pairs. These w ↔ WC tautomerisations occur non-dissociatively and are accompanied by a significant alteration in geometry (from wobble to Watson–Crick and vice versa) and redistribution of the specific intermolecular interactions, which can be divided into 10 patterns including AH⋯B H-bonds and loosened A–H–B covalent bridges along the IRC of tautomerisation. Based on the redistribution of the geometrical and electron-topological parameters of the intrapair hydrogen bonds, exactly 9 key points have been allocated to characterize the evolution of these reactions.

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Introduction

Establishment of the fundamental mechanisms of the origin of point mutations induced by analogues of DNA bases is an intriguing topic in biophysics of DNA due to their importance in human health and numerous technical applications.^1–8

To date, several experimental^9–22 and theoretical^23–26 studies have reported the mechanisms of action of the classic mutagen 2-aminopurine (2AP), which is also used as a fluorescent probe,^18–21 inducing A·T → G·C and G·C → A·T transitions.^11,12 However, these results are essentially independent and do not represent a complete picture of the mechanisms of the origin of the point mutations in DNA induced by 2AP.

In recent papers,^27–35 a solution of this extremely important and very difficult biological problem was comprehensively and thoroughly addressed by analyzing the structural mechanisms of the 2AP mutagenic pressure on DNA due to the latest breakthrough in the precise understanding of the origin of spontaneous point mutagenesis in DNA^36–42 within the framework of the classical Watson–Crick tautomeric hypothesis.⁴³

Moreover, our theoretical data on spontaneous point mutations and that induced by analogues of the DNA bases, in particular transitions and transversions, are in good agreement with the experimental observations.^{9–22,44–48}

In particular, our results prove that 2AP produces transversions by forming a wobble (w) mispair with A DNA base, A·2AP(w), followed by further A·2AP(w) → A*·2AP(WC) (WC – Watson–Crick) tautomerisation and subsequent A*·2AP(WC) → A*·2AP_syn conformational transition, thus acquiring the A*·2AP_syn enzymatically-competent conformation³³ (herein, the asterisk denotes the mutagenic tautomers of the DNA bases^49–57).

It was also shown for the first time that 2AP* may also produce another transversion when the 2AP* mutagenic tautomer pairs with the G base to form the G·2AP*(w) mispair, which converts to the G·2AP_syn enzymatically-competent structure via consecutive tautomeric and conformational transformations: G·2AP*(w) → G*·2AP(w) → G·2AP(WC) → G·2AP_syn.³² In this case, the long G·2AP(WC) WC-like mispair acts as a precursor to the enzymatically-competent conformation, the G·2AP_syn mispair.

The estimated ratio of probabilities P_A·2AP/P_A·A = 40.5³³ and P_G·2AP*/P_G·A* = 1.9 × 10^7 32 indicates that these structural transformation routes are mutagenic. Notably, the formed A*·2AP_syn and G·2AP_syn base pairs quite easily acquire an enzymatically-competent WC conformation during the process of thermal fluctuations, which enables their successful incorporation into the DNA double helix by the high-fidelity replicative DNA-polymerase.

The present work presents a detailed quantum-mechanical/Quantum Theory of Atoms in Molecules (QM/QTAIM) investigation of the physico-chemical parameters at each point of the intrinsic reaction coordinate (IRC) of the acquisition by the G*·2AP(w) and A·2AP(w) nucleobase mispairs involving the 2AP mutagen^27–30 with Watson–Crick geometry due to the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations. This investigation enables the monitoring of the energetic, polar, geometric, charge, electron-topological and natural bond orbital (NBO) characteristics of the base mispairs and intrapair interactions along the IRC. It is worthy to note that the profiles of the geometric parameters, including the distance R(H₉–H₉) between the H₉ and H₉ glycosidic hydrogens, glycosidic angles α₁/α₂, d_A⋯B distances between the electronegative A and B atoms, ∠AH⋯B angles of the AH⋯B hydrogen (H) bonds and patterns of the energy of the intermolecular H-bonds E_HB indicate significant rebuilding of the geometry of the nucleobase pairs and the non-dissociative character of these biologically important w ↔ WC tautomerisations, which occur without breakage of the pairs. Using the obtained evolutions of the physico-chemical parameters along the IRC, 9 key points (KPs) have been established, which allow the phases of the reactions to be distinguish and demonstrate that in the course of these w ↔ WC tautomerisations, protons move sequentially without a stable intermediate, followed by spatial rearrangement of the nucleobases relative to each other within the base pairs.

Computational methods

All calculations were performed using the Gaussian'09 program package.⁵⁸ The geometries and harmonic vibrational frequencies of the considered base mispairs and transition states (TSs) of their mutual tautomeric conversions were obtained in our previous work at the B3LYP/6-311++G(d,p) level of theory, which suggested that it is suitable for the investigation of similar systems,^59,60 followed by single point energy calculations at the MP2/aug-cc-pVDZ level of theory.^27–35

In order to consider the surrounding effect on the investigated tautomerisation processes, we used the conductor-like polarizable continuum model (CPCM),^61,62 choosing the continuum with a dielectric constant ε = 4, which is typical for the active center of DNA-polymerase.^63,64

The reaction pathway for the proton transfer (PT) tautomerisation of the wobble base mispairs was obtained by following the IRC in the forward and reverse directions from the transition state (TS) using the Hessian-based predictor–corrector integration algorithm⁶⁵ with tight convergence criteria. We obtained the profiles of the energetic, geometric, polar, charge, electron-topological and NBO characteristics of the H-bonds and complexes along the pathway of the tautomerisation reactions by calculating them at each point of the IRC using our previously reported methodology.^66–70 The profiles of the NBO charges along the IRC were obtained using the NBO program,⁷¹ which was implemented in the Gaussian'09⁵⁸ program package.

Bader's quantum theory of atoms in molecules (QTAIM) was applied to analyse the electron density distribution⁷² using the program package AIMAll⁷³ 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 H-bond formation.⁷⁴ Wave functions were obtained at the level of theory used for geometry optimisation.

The H-bond energy, E_HB, was calculated using the empirical Espinosa–Molins–Lecomte (EML) formula^75,76 based on the electron density distribution at the (3,−1) BCPs of the H-bonds:

E_HB = 0.5·V(r)

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

The atomic numbering scheme for the nucleotide bases is conventional.⁷⁷

Results and discussion

Exhaustive analysis of the potential energy surface

Comprehensive analysis of the potential energy surface and IRC calculations revealed that the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations occur via the initial transfer of the single proton localized at the O6/N6 atoms of the G*/A DNA bases in the wobble G*·2AP(w)/A·2AP(w) mispairs along the upper O6/N6H⋯N1 H-bonds to the 2AP base followed by the shifting of the 2AP base according the G*/A DNA bases into the minor groove of DNA. This results in the localized transition states TS^G−·2AP+_{G*·2AP(w)↔G·2AP(WC)}/TS^A−·2AP+_{A·2AP(w)↔A*·2AP(WC)} since the G⁻/A⁻·2AP⁺ tight ion pairs are stabilized by the participation of the network of the C6⁺H⋯O6⁻/N6⁻, N1⁺H⋯O6⁻/N6⁻, N1⁺H⋯N1⁻, N2⁺H⋯N1⁻, and N2⁺H⋯N2⁻ H-bonds (Fig. 1 and 5) with the ΔΔG_TS/ΔΔE_TS barriers of 18.04/16.58 and 29.85/31.00 kcal mol⁻¹ (Tables 2–5), respectively. Further, the reagent complexes finally acquire the Watson–Crick geometry and the mobile proton at the N1 atom of the 2AP⁺ base moves back to the N1 atom of the G*/A DNA bases along the middle N1H⋯N1 H-bond. This compensates the excessive charge of the 2AP⁺ nucleobase and leads to the formation of the G·2AP(WC)/A*·2AP(WC) Watson–Crick-like nucleobase mispairs joined by the C6H⋯O6/N6, N1H⋯N1, and N2/C2H⋯N2/HN2 H-bonds with relative ΔΔG/ΔΔE energies of 1.33/1.07 and 13.71/13.57 kcal mol⁻¹ (Table 1), respectively. It was established that for the minima, which are the initial G*·2AP(w)/A·2AP(w) and terminal G·2AP(WC)/A*·2AP(WC) complexes, all frequencies of the normal vibrations are real, whereas the TSs possess one imaginary frequency, corresponding to the shifting motion of the bases relative to each other into the minor and major DNA grooves.

Fig. 1 Geometrical structures of the 9 key points describing the evolution of the G*·2AP(w) ↔ G·2AP(WC) w ↔ WC tautomerisation via the sequential PT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo. The coordinates of the 9 key points, their relative Gibbs free energies ΔG or relative electronic energies ΔE (in kcal mol⁻¹ obtained at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1 at T = 298.15 K) and imaginary frequencies ν_i (cm⁻¹) at the TSs of their interconversions are presented below them in brackets. The dotted lines indicate AH⋯B H-bonds, while the continuous lines show covalent bonds (their lengths are presented in angstroms). Carbon atoms are in light-blue, nitrogen in dark-blue, hydrogen in grey and oxygen in red.

Table 1 Energetic and kinetic characteristics of the biologically important tautomerisations of the investigated mispairs containing purine canonical DNA bases and 2-aminopurine nucleobase in the main or rare tautomeric forms leading to incorporation and replication errors (MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1 and ε = 4) (see also Fig. S1, ESI)

Tautomeric transformation	ν i	ΔG^b	ΔE^c	ΔΔGTS^d	ΔΔETS^e	ΔΔG^f	ΔΔE^g	k f	k r	τ 99.9%	τ
Note:a Imaginary frequency at the TSs of the tautomerisation reaction, cm^−1.b The Gibbs free energy of the product relative to the reactant of the tautomerisation reaction (T = 298.15 K), kcal mol^−1.c The electronic energy of the product relative to the reactant of the tautomerisation reaction, kcal mol^−1.d The Gibbs free energy barrier for the forward reaction of tautomerisation, kcal mol^−1.e The electronic energy barrier for the forward reaction of the tautomerisation, kcal mol^−1.f The Gibbs free energy barrier for the reverse reaction of the tautomerisation, kcal mol^−1.g The electronic energy barrier for the reverse reaction of the tautomerisation, kcal mol^−1.h The forward rate constant for the tautomerisation reaction, s^−1.i The reverse rate constant for the tautomerisation reaction, s^−1.j The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerization reaction, s.k The lifetime of the product of the tautomerisation reaction, s.
ε = 1
G*·2AP(w) ↔ G·2AP(WC)	130.1	1.33	1.07	18.04	16.58	16.70	15.51	0.37	3.53	1.77	0.28
G*·A(w) ↔ G·A(WC)	107.2	−4.30	−6.73	12.33	9.97	16.64	16.70	5.64 × 10^3	3.94	1.22 × 10^−3	0.25
A·2AP(w) ↔ A*·2AP(WC)	117.0	13.71	13.57	29.85	31.00	16.14	17.43	8.01 × 10^−10	9.10	0.76	0.11
A·A(w) ↔ A*·A(WC)	152.4	3.63	1.09	25.86	22.56	22.24	21.47	6.79 × 10^−7	3.10 × 10^−4	2.22 × 10^4	3.22 × 10^3
ε = 4
G*·2AP(w) ↔ G·2AP(WC)	104.6	−1.20	−1.09	12.30	11.61	13.50	12.71	5.93 × 10^3	7.80 × 10^2	1.03 × 10^−3	1.28 × 10^−3
G*·A(w) ↔ G·A(WC)	84.5	−4.87	−6.90	8.42	6.08	13.29	12.98	4.20 × 10^6	1.11 × 10^3	8.97 × 10^−4	1.65 × 10^−6
A·2AP(w) ↔ A*·2AP(WC)	95.9	12.62	11.88	26.53	26.33	13.91	14.45	2.18 × 10^−7	3.95 × 10^2	1.75 × 10^−2	2.53 × 10^−3
A·A(w) ↔ A*·A(WC)	108.3	6.82	2.37	21.82	19.19	15.01	16.82	6.17 × 10^−4	61.71	0.11	1.62 × 10^−2

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Table 2 Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latter along the IRC of the G*·2AP(w) ↔ G·2AP(WC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1

Complex	AH⋯B H-bond/A–H/H–B covalent bond	ρ	Δρ^b	100·ε^c	d A⋯B	d H⋯B	∠AH···B^f	μ
Notes:a The electron density at the (3,−1) BCP, a.u.b The Laplacian of the electron density at the (3,−1) BCP, a.u.c The ellipticity at the (3,−1) BCP.d The distance between the A (H-bond donor) and B (H-bond acceptor) atoms of the AH⋯B H-bonds, Å.e The distance between the H and B atoms of the AH⋯B H-bonds, Å.f The H-bond angle, degree.g The dipole moment of the complex, D.
Key point 1 (−17.65 Bohr): G*·2AP(w)	O6H⋯N1	0.049	0.100	5.14	2.728	1.735	168.4	4.58
	N1⋯HN2	0.026	0.077	7.43	3.029	2.016	171.3
Key point 2 (−4.54 Bohr): ΔρH⋯N1 = 0	O6H⋯N1	0.126	−0.037	3.27	2.492	1.359	164.3	5.64
	N1⋯HN2	0.025	0.076	6.60	2.989	2.035	155.0
Key point 3 (−4.30 Bohr): ρO6–H = ρH–N1	O6–H/H–N1	0.169	−0.317	2.79	2.500	1.250	161.9	6.82
	N1⋯HN2	0.025	0.075	6.65	2.989	2.034	154.8
Key point 4 (−4.18 Bohr): ΔρO6⋯H = 0	O6⋯HN1	0.124	0.008	2.25	2.507	1.341	160.5	7.41
	N1⋯HN2	0.025	0.074	6.64	2.990	2.035	154.6
Key point 5 (0.00 Bohr): TS^G−·2AP+G*·2AP(w)↔G·2AP(WC)	O6^−⋯HC6^+	0.013	0.049	67.40	2.961	2.380	112.0	10.62
	O6^−⋯HN1^+	0.028	0.092	26.10	2.754	1.963	129.7
	N1^−⋯HN1^+	0.031	0.088	6.86	2.910	1.915	156.9
	N1^−⋯HN2^+	0.014	0.045	8.67	3.166	2.318	139.9
	N2^−⋯HN2^+	0.013	0.044	9.18	3.240	2.286	155.5
Key point 6 (6.63 Bohr): ΔρN1⋯H = 0	O6⋯HC6	0.018	0.064	7.54	2.963	2.179	127.1	9.50
	N1⋯HN1	0.104	0.006	4.74	2.628	1.450	173.5
	N2⋯HN2	0.025	0.072	5.73	3.039	2.033	167.3
Key point 7 (6.99 Bohr): ρN1–H = ρH–N1	O6⋯HC6	0.018	0.064	7.52	2.965	2.182	127.0	8.47
	N1–H/H–N1	0.145	−0.168	3.56	2.612	1.317	172.4
	N2⋯HN2	0.025	0.073	6.23	3.038	2.038	166.5
Key point 8 (7.24 Bohr): ΔρH⋯N1 = 0	O6⋯HC6	0.017	0.063	7.64	2.967	2.188	126.7	7.79
	N1H⋯N1	0.105	0.024	4.32	2.610	1.443	170.9
	N2⋯HN2	0.025	0.074	6.51	3.039	2.042	166.3
Key point 9 (17.65 Bohr): G·2AP(WC)	O6⋯HC6	0.010	0.029	2.90	3.366	2.470	138.9	7.72
	N1H⋯N1	0.033	0.088	6.76	2.948	1.916	176.2
	N2⋯HN2	0.008	0.026	110.77	3.400	2.654	130.7

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Table 3 Patterns of the specific intermolecular interactions including AH⋯B H-bonds and loosened A–H–B covalent bridges that sequentially replace each other along the IRC of the G*·2AP(w) ↔ G·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1

Patterns	IRC range, Bohr	Specific intermolecular interactions, forming patterns
I	[−17.65 to −4.54)	(G)O6H⋯N1(2AP), (G)N1⋯HN2(2AP)
II	[−4.54 to −4.18)	(G)O6-H-N1(2AP), (G)N1⋯HN2(2AP)
III	[−4.18 to −2.46)	(G)O6⋯HN1(2AP), (G)N1⋯HN2(2AP)
IV	[−2.46 to −1.97)	(G)O6⋯HN1(2AP), (G)N1⋯HN2(2AP), (G)N2⋯HN2(2AP)
V	[−1.97 to −0.86)	(G)O6⋯HN1(2AP), (G)N1⋯HN1(2AP), (G)N1⋯HN2(2AP), (G)N2⋯HN2(2AP)
VI	[−0.86 to 2.21)	(G)O6⋯HC6(2AP), (G)O6⋯HN1(2AP), (G)N1⋯HN1(2AP), (G)N1⋯HN2(2AP), (G)N2⋯HN2(2AP)
VII	[2.21 to 3.56)	(G)O6⋯HC6(2AP), (G)N1⋯HN1(2AP), (G)N1⋯HN2(2AP), (G)N2⋯HN2(2AP)
VIII	[3.56 to 6.75)	(G)O6⋯HC6(2AP), (G)N1⋯HN1(2AP), (G)N2⋯HN2(2AP)
IX	[6.75 to 7.24)	(G)O6⋯HC6(2AP), (G)N1-H-N1(2AP), (G)N2⋯HN2(2AP)
X	[7.24 to 17.65]	(G)O6⋯HC6(2AP), (G)N1H⋯N1(2AP), (G)N2⋯HN2(2AP)

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Table 4 Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latter along the IRC of the A·2AP(w) ↔ A*·2AP(WC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1

Complex	AH⋯B H-bond/A–H/H–B covalent bond	ρ	Δρ	100·ε	d A···B	d H···B	∠AH···B	μ
Notes: for footnote definitions see Table 2.
Key point 1 (−18.38 Bohr): A·2AP(w)	N6H⋯N1	0.029	0.081	7.56	3.002	1.976	179.4	1.09
	N1⋯HN2	0.026	0.076	7.89	3.043	2.021	179.7
Key point 2 (−5.21 Bohr): ΔρH⋯N1 = 0	N6H⋯N1	0.105	0.033	3.41	2.598	1.426	171.9	3.37
	N1⋯HN2	0.028	0.083	7.18	2.957	1.977	159.5
Key point 3 (−4.96 Bohr): ρN6–H = ρH–N1	N6–H/H–N1	0.142	−0.146	2.79	2.602	1.313	168.7	4.91
	N1⋯HN2	0.029	0.082	7.20	2.957	1.974	159.5
Key point 4 (−4.60 Bohr): ΔρN6⋯H = 0	N6⋯HN1	0.098	0.011	4.80	2.621	1.475	163.0	7.06
	N1⋯HN2	0.029	0.080	7.18	2.959	1.974	159.2
Key point 5 (0.00 Bohr): TS^A−·2AP+A·2AP(w)↔A*·2AP(WC)	N6^−⋯HC6^+	0.016	0.052	9.19	3.023	2.344	119.0	9.98
	N6^−⋯HN1^+	0.020	0.071	47.64	2.887	2.131	126.4
	N1^−⋯HN1^+	0.039	0.089	1.05	2.860	1.834	162.3
	N1^−⋯HN2^+	0.015	0.048	4.15	3.154	2.277	144.0
Key point 6 (4.00 Bohr): ΔρN1⋯H = 0	N6⋯HC6	0.020	0.063	1.63	3.012	2.205	129.1	8.54
	N1⋯HN1	0.097	0.016	4.34	2.661	1.482	179.2
	C2H⋯HN2	0.008	0.029	25.88	2.689	2.049	114.3
Key point 7 (4.35 Bohr): ρN1–H = ρH–N1	N6⋯HC6	0.020	0.063	1.55	3.014	2.209	129.0	6.98
	N1–H/H–N1	0.145	−0.181	3.36	2.645	1.317	177.8
Key point 7 (4.60 Bohr): ΔρH⋯N1 = 0	C2H⋯HN2	0.008	0.028	18.64	2.701	2.051	115.2
Key point 8 (4.60 Bohr): ΔρH⋯N1 = 0	N6⋯HC6	0.019	0.063	1.45	3.015	2.215	128.6	5.79
	N1H⋯N1	0.106	0.012	4.02	2.642	1.440	176.2
	C2H⋯HN2	0.008	0.028	15.70	2.704	2.052	115.4
Key point 9 (16.31 Bohr): A*·2AP(WC)	N6⋯HC6	0.013	0.039	5.58	3.332	2.388	144.2	4.55
	N1H⋯N1	0.029	0.082	7.01	2.991	1.961	175.2
	C2H⋯HN2	0.001	0.005	75.42	3.668	2.987	125.7

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Table 5 Patterns of the specific 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·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1

Patterns	IRC range, Bohr	Specific intermolecular interactions, forming patterns
I	[−18.34 to −5.09)	(A)N6H⋯N1(2AP), (A)N1⋯HN2(2AP)
II	[−5.09 to −4.60)	(A)N6–H–N1(2AP), (A)N1⋯HN2(2AP)
III	[−4.60 to −3.51)	(A)N6⋯HN1(2AP), (A)N1⋯HN2(2AP)
IV	[−3.51 to −2.91)	(A)N6⋯HN1(2AP), (A)N1⋯HN1(2AP), (A)N1⋯⋯HN2(2AP)
V	[–2.91 to 1.21)	(A)N6⋯HC6(2AP), (A)N6⋯HN1(2AP), (A)N1⋯HN1(2AP), (A)N1⋯HN2(2AP)
VI	[1.21 to 2.30)	(A)N6⋯HC6(2AP), (A)N1⋯HN1(2AP), (A)N1⋯HN2(2AP)
VII	[2.30 to 3.26)	(A)N6⋯HC6(2AP), (A)N1⋯HN1(2AP), (A)N1⋯HN2(2AP), (A)C2H⋯HN2(2AP)
VIII	[3.26 to 4.23)	(A)N6⋯HC6(2AP), (A)N1⋯HN1(2AP), (A)C2H⋯HN2(2AP)
IX	[4.23 to 4.60)	(A)N6⋯HC6(2AP), (A)N1–H–N1(2AP), (A)C2H⋯HN2(2AP)
X	[4.60 to 16.31]	(A)N6⋯HC6(2AP), (A)N1H⋯N1(2AP), (A)C2H⋯HN2(2AP)

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Analysis of the potential energy surface shows that these reactions proceed through the sequential intrapair PT.

The profiles of the electronic energy of the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) tautomerisation reactions are quite smooth in the vicinity of the TSs. In contrast, peaks and fractures are present on both sides of the TSs, which correspond to the range of existence of the G⁻/A⁻·2AP⁺ ion pairs during their transformations, namely to KP 4 and KP 6 (Fig. 2a and 6a, respectively).

The transition from vacuum to weakly polar continuum with ε = 4, which is typical for the interfaces of specific protein–nucleic acid interactions, does not qualitatively affect the course and structure of the transition state of the tautomerisation reactions (Fig. S1, ESI†). This could be explained by the fact that this transition does not disturb the structure of the TSs of these tautomerisations, since it is a highly stable, tight ion pair. Simultaneously, this transition accelerates the w ↔ WC tautomerisation, while the shape of the curves dependent on the energy of the studied pairs from the IRC does not significantly change (Fig. S1, ESI†).

The calculated first derivatives of the electronic energy E by the IRC, in particular, the peaks on its curve, enable the reaction pathways of these reactions to be divided into regions of reagent (13.11/13.17 Bohr), transition state (11.78/9.81 Bohr) and product (10.41/11.71 Bohr) based on the data collected by us^31–37 and our colleagues^78–80 (Fig. 2b and 6b). The widest is the preparation reagent stage corresponding to the intrapair proton transfer, whereas the narrowest is the TS region, where mutual reorientation and shifting of the bases relative to each other occur. Consequently, the direct initiation of the G*·2AP(w) → G·2AP(WC) and A·2AP(w) → A*·2AP(WC) reactions requires the electronic energy ΔE_KP2 − ΔE_{KP1[G*·2AP(w)/A·2AP(w)]} = 10.60/18.75 kcal mol⁻¹, which represents 57.3%/56.4% of the electronic energies of the TSs. In contrast, much less energy is required for the final relaxation of the reaction complexes to the terminal mispairs: ΔE_KP8 − ΔE_{KP9[G·2AP(WC)/A*·2AP(WC)]} = 8.71/13.85 kcal mol⁻¹, which represents 47.1%/41.4% of the energies of TS^G−·2AP+_{G*·2AP(w)↔G·2AP(WC)}/TS^A−·2AP+_{A·2AP(w)↔A*·2AP(WC)}. These observations indicate that more energy is required to initiate the reaction due to the preparatory PT before the structurally-electronic rebuilding of the nucleobases within the mispairs in the TS region, especially in the case of the A·2AP(w) → A*·2AP(WC) w → WC tautomerisation (∼2 times), than for the final relaxation to the terminal mispairs (Fig. 2b).

The established data show the resemblance between the courses of these processes and their electronic energy profiles regardless of their structural difference (Fig. 1, 2, 5 and 6). Notably, these conversions with the participation of the 2AP analogue are established to be the same as that with the participation of the canonical A DNA bases G*·A(w) ↔ G·A(WC)⁴¹ and A·A(w) ↔ A*·A(WC)⁴² (Table 1).

Polar and charge characteristics

The profiles of the dipole moment reflecting the changes in the polarities along the IRC are bell-shaped near the TS (4.40–10.67/1.04–10.00 D) and almost plateau on each side of it with average values of 4.56/1.11 D on the left and 7.43/4.75 D on the right (Fig. 2c and 6c), respectively.

The calculated profiles of the NBO charges (0.402–0.508/0.375–0.493 e) of the hydrogen atoms involved in the intermolecular H-bonds are dome-shaped in the TS region with fractures, whereas they are almost constant lines at the beginning and ending of these tautomerisation reactions (Fig. 2d and 6d, respectively). The notable feature of the A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation is that the NBO charges for the H atoms located at the N2 and N6 atoms coincide at the beginning of the reaction (0.435 and 0.434 e), while their difference increases at the ending of the reaction (0.384 and 0.451 e) (Fig. 2d and 6d), respectively.

Geometric and electron-topological characteristics of the mispairs and intermolecular H-bonds

Using our previously reported methodology^81–85 we calculated the changes in the main physico-chemical characteristics at each point of the IRC, which are presented in Fig. 2–4 and 6–8, respectively.

Fig. 2 Profiles of (a) relative electronic energy ΔE together with the stationary states (G*·2AP(w), TS^G−·2AP+_{G*·2AP(w)↔G·2AP(WC)}, G·2AP(WC)) and KPs 4 and 6, (b) first derivative of the electronic energy with respect to the IRC (dE/dIRC), (c) dipole moment μ, (d) NBO charges q_NBO, (e) distance R(H₉–H₉) between the H₉ and H₉ glycosidic hydrogens and (f) α₁ (∠N9H₉(2AP)H₉(G)) and α₂ (∠N9H₉(G)H₉(2AP)) glycosidic angles along the IRC of the G*·2AP(w) ↔ G·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1.

Fig. 3 Profiles of (a) electron density ρ; (b) Laplacian of the electron density Δρ, (c) ellipticity ε at the (3,−1) BCPs, (d) distance d_A⋯B between the electronegative A and B atoms; (e) distance d_AH/HB between the hydrogen and electronegative A or B atoms and (f) angle ∠AH⋯B of the H-bonds along the IRC of the G*·2AP(w) ↔ G·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1.

Fig. 4 Profiles of the energy of the intermolecular H-bonds E_HB estimated by the EML formula at the (3,−1) BCPs along the IRC of the G*·2AP(w) ↔ G·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1 (see Table 3).

Fig. 5 Geometric structures of the 9 key points describing the evolution of the A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation via the sequential PT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1. For designations see Fig. 1.

Fig. 6 Profiles of (a) relative electronic energy ΔE together with stationary states (A·2AP(w), TS^A−·2AP+_{A·2AP(w)↔A*·2AP(WC)}, A*·2AP(WC)) and KPs 4 and 6, (b) first derivative of the electronic energy with respect to the IRC (dE/dIRC), (c) dipole moment μ, (d) NBO charges q_NBO, (e) distance R(H₉–H₉) between the H₉ and H₉ glycosidic hydrogens and (f) α₁ (∠N9H₉(2AP)H₉(A)) and α₂ (∠N9H₉(A)H₉(2AP)) glycosidic angles along the IRC of the A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1.

Fig. 7 Profiles of (a) electron density ρ; (b) Laplacian of the electron density Δρ, (c) ellipticity ε at the (3,−1) BCPs, (d) distance d_A⋯B between the electronegative A and B atoms; (e) distance d_AH/HB between the hydrogen and electronegative A or B atoms and (f) angle ∠AH⋯B of the AH⋯B H-bonds along the IRC of the A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1.

Fig. 8 Profiles of the energy of the intermolecular H-bonds E_HB estimated by the EML formula at the (3,−1) BCPs along the IRC of the A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisation via the sequential PT obtained at the B3LYP/6-311++G(d,p) level of theory in the continuum with ε = 1 (see Table 5).

Based on the evolution of the geometrical parameters (R(H₉–H₉), d_AH/HB and d_A⋯B distances, α₁/α₂ and ∠AH⋯B angles) along the IRC, it was found that the investigated reactions are followed by significant geometry changes in the base pairs, thus reflecting the large-scale movement of the bases relative to each other within the mispairs (Fig. 2e, f, 3d–f, 6e, f and 7d–f). The distinguished feature of the profiles of the glycosidic distances R(H₉–H₉) (11.805–12.506/12.142–12.766 Å), distances between the hydrogen and electronegative atoms d_AH/HB (1.004–3.353/1.003–3.696 Å), distances between the electronegative atoms d_A⋯B (2.490–4.023/2.597–4.209 Å) and angles of the H-bonding ∠AH⋯B (89.4–173.9/89.0–179.7°) is the presence of kinks in the vicinity of the 2^nd and 8^th key points, which could be associated with the structural changes in the base mispairs from the wobble to the Watson–Crick architecture due to the shifting of the 2AP base downwards into the minor DNA groove according the G*/A bases. The same tendencies have also been observed for the 2AP·T(WC) ↔ 2AP·T*(w) and 2AP·C*(WC) ↔ 2AP·C(w) WC ↔ w tautomeric transformations.³⁴

The curves of the α₁ glycosidic angle of 2AP gradually decrease, whereas the curves of the α₂ glycosidic angle of the G*/A bases gradually increase along the IRC, which vary in a broad range of values (30.3–51.7/31.7–53.3°) and equalize (41.2/39.7°) at IRC = 13.11/8.57 Bohr (Fig. 2f and 6f, respectively).

The calculations of the profiles of the electron-topological parameters at each point of the IRC, namely the electron density ρ (0.009–0.316/0.001–0.322 a.u.) and Laplacian of the electron density Δρ (−2.141–0.124/−1.703–0.127 a.u.), as well as the d_AH/HB distances reveal their crossings at the transformations of the H-bonds along the IRC: (G/A)O6/N6H⋯N1(2AP) → (G/A)O6/N6⋯HN1(2AP) and (G/A)N1⋯HN1(2AP) → (G/A)N1H⋯N1(2AP) (Fig. 3a, b, e, 7a, b and e). These data correspond to the maximal and minimal values of ρ (0.169/0.142 and 0.145/0.145 a.u.), Δρ (−0.317/−0.146 and −0.168/−0.181 a.u.) and d_AH/HB (1.250/1.313 and 1.317/1.317 Å) and enable the 2 key points containing loosened O6/N6–H–N1 and N1–H–N1 covalent bridges to be distinguished (Fig. 1 and 5), respectively, which are the 3^rd (−4.30/−4.96 Bohr) and 7^th (6.99/4.35 Bohr) key points. Another 4 key points have been allocated as that where the Laplacian of the electron density Δρ equals zero, that is the H-bond converts to a covalent bond and vice versa, which are the 2^nd (−4.54/−5.21 Bohr), 4^th (−4.18/−4.60 Bohr), 6^th (6.63/4.00 Bohr) and 8^th (7.24/4.60 Bohr) key points. The other 3 key points, the 1^st, 5^th and 9^th, represent stationary structures of the initial wobble G*·2AP(w)/A·2AP(w) base mispairs, the TS^G−·2AP+_{G*·2AP(w)↔G·2AP(WC)}/TS^A−·2AP+_{A·2AP(w)↔A*·2AP(WC)} transition states and terminal Watson–Crick-like G·2AP(WC)/A*·2AP(WC) base mispairs (Fig. 1 and 5) respectively.

The profiles of the ellipticity ε at the (3,−1) BCPs of the (G/A)N1⋯HN2(2AP), (G/A)O6/N6⋯HC6(2AP), (G/A)N2/C2H⋯N2/HN2(2AP) intermolecular H-bonds gradually increase or decrease along the IRC, rapidly reaching their maxima on the borders, whereas the (G/A)O6/N6H⋯N1(2AP) and (G/A)N1H⋯N1(2AP) H-bonds remain almost stable along the IRC (Fig. 3c and 7c, respectively).

Similarly to the previously investigated 2AP·T(WC) ↔ 2AP·T*(w) and 2AP·C*(WC) ↔ 2AP·C(w) WC ↔ w tautomeric transformations,³⁴ the calculated evolutions of the energies E_HB of the intermolecular H-bonds could be divided into 10 patterns which sequentially change each other along the IRC (Tables 3, 5 and Fig. 4, 8).

The G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations are accompanied by the formation and breakage of the intermolecular H-bonds, including simultaneously maximum 5 H-bonds in the first case, (G)O6⋯HC6(2AP), (G)O6⋯HN1(2AP), (G)N1⋯HN1(2AP), (G)N1⋯HN2(2AP) and (G)N2⋯HN2(2AP), within the ranges of IRC −0.86 to 2.21 Bohr and 4 H-bonds in the second case, (A)N6⋯HC6(2AP), (A)N6⋯HN1(2AP), (A)N1⋯HN1(2AP) and (A)N1⋯HN2(2AP) and (A)N6⋯HC6(2AP), (A)N1⋯HN1(2AP), (A)N1⋯HN2(2AP) and (A)C2H⋯HN2(2AP), within the ranges of IRC from −2.91 to 1.21 and from 2.30 to 3.26 Bohr, respectively. The curves of the (G/A)O6/N6H⋯N1(2AP) and (G/A)N1⋯HN1(2AP) H-bonds gradually increase from 13.19/6.10 to 37.64/36.11 and from 5.22/4.29 to 33.36/33.74 kcal mol⁻¹, curves of the (G/A)O6/N6⋯HN1(2AP) and (G/A)N1H⋯N1(2AP) H-bonds gradually decrease from 45.66/30.37 to 4.47/3.57 and from 34.90/36.64 to 7.86/6.11 kcal mol⁻¹, while the profiles of the (G/A)N1⋯HN2(2AP), (G/A)O6/N6H⋯N1(2AP) and (G/A)N2/C2H⋯HN2(2AP) H-bonds monotonically change along the IRC reaching their maximal values at the borders of the II and III (5.47/6.25 kcal mol⁻¹), VIII and IX (3.56/3.58 kcal mol⁻¹), and IX and X regions (5.04/1.36 kcal mol⁻¹) (Fig. 4 and 8, Tables 3 and 5).

It is worth mentioning that at the beginning of the A·2AP(w) ↔ A*·2AP(WC) reaction, the geometrical, energetic and electron-topological parameters almost coincide, that demonstrates their close values (Fig. 3, 4, 7 and 8, and Tables 2 and 4).

Close comparison of the obtained profiles for the w ↔ WC tautomeric conversions with the participation of the 2AP nucleobase analogue (Fig. 2–4, 6–8 and Fig. S1, ESI†) and canonical DNA bases^40,41 reflects high similarity between the courses of these processes and their scanning along the IRC. This represents an especially valuable observation since it could be used for the extension of the data for the canonical conversions to that with the participation of 2AP.

Notably, in all considered tautomerisation reactions, we did not fix the non-planar deformations of the DNA bases, despite their susceptibility to such processes.^86–88

Conclusions

The current study is intended to give insight into the physico-chemical mechanism of the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations, which are involved into the mutagenic G·2AP*(w) → G*·2AP(w) → G·2AP(WC) → G·2AP_syn^32,35 and A·2AP(w) → A*·2AP(WC) → A*·2AP_syn³³ tautomerically-conformational pathways originating from the induced transitions and transversions.

The profiles of the electronic energy E, the first derivative of the electronic energy with respect to the IRC, dE/dIRC, the dipole moment of the base pair μ, the NBO charges q_NBO of the hydrogen atoms involved in the tautomerisations, the distance R(H₉–H₉) between the H₉ glycosidic hydrogens, the glycosidic angles α₁/α₂, the electron density ρ, the Laplacian of the electron density Δρ and the ellipticity ε at the (3,−1) BCPs of the intrapair covalent and hydrogen bonds, the distances d_A⋯B, d_AH/HB, the angles ∠AH⋯B and the energy of the intermolecular H-bonds E_HB along the IRC were established.

This detailed analysis enabled us to follow all the changes in the physico-chemical characteristics, including energetic, structural, polar, charge, and electron-topological, along the IRC at each point of these reactions. Moreover, it was found that the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations proceed via the followed by the subsequent shifting of the G/A and 2AP bases relative to each other.

Nine key points along the IRC were established, three of them (1st, 5th and 9th) correspond to the stationary structures and the six others (2nd, 3rd, 4th, 6th, 7th and 8th) reflect the rearrangement of the intermolecular H-bonds, O6/N6H⋯N1, N2H⋯N1 (G*·2AP(w)/A·2AP(w)) → C6⁺H⋯O6⁻/N6⁻, N1⁺H⋯O6⁻/N6⁻, N1⁺H⋯N1⁻, N2⁺H⋯N1⁻, N2⁺H⋯N2⁻ (TS^G−·2AP+_{G*·2AP(w)↔G·2AP(WC)}/TS^A−·2AP+_{A·2AP(w)↔A*·2AP(WC)}) → C6H⋯O6/N6, N1H⋯N1 and N2/C2H⋯N2/HN2 (G·2AP(WC)/A*·2AP(WC)), which are grouped into 10 patterns of interactions including AH⋯B H-bonds and loosened A–H–B covalent bridges.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully appreciate technical support and computational facilities of joint computer cluster of SSI “Institute for Single Crystals” of the National Academy of Sciences of Ukraine (NASU) and Institute for Scintillation Materials of the NASU incorporated into the Ukrainian National Grid. This work was partially supported by the Grant of the NASU for young scientists for 2017 year, Grant of the President of Ukraine to support the research of young scientists [project number F70] from the State Fund for Fundamental Research of Ukraine of the Ministry of the Education and Science of Ukraine and by the Personal Scholarship of Verkhovna Rada (Parliament) of Ukraine for the talented young scientists in 2017 year given to DrSci Ol'ha O. Brovarets'. O. O. B. expresses sincere gratitude to organizing committee for financial support of the participation in the “EMBO/FEBS Lecture Course Spetsai Summer School 2017 for Proteins and Organized Complexity” (September 24–October 1, 2017, Spetses, Greece), to Lawyers Association “AVER Lex” (Kyiv, Ukraine) for the sponsorship of the presenting the plenary lecture as invited speaker at the “EMN Meeting on Computation and Theory” (November 6–10, 2017, Dubai, United Arab Emirates) and to Max Planck Institute of Plant Physiology (hosted by Dr. Yariv Brotman) for the invitation and financial support of the invited talk (November 29, 2017, Potsdam, Germany).

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Footnote

† Electronic supplementary information (ESI) available: Profiles of the relative electronic energy along the IRC of the G*·2AP(w) ↔ G·2AP(WC) and A·2AP(w) ↔ A*·2AP(WC) w ↔ WC tautomerisations in the continuum with ε = 4, characteristic of the active center of the DNA-polymerase. See DOI: 10.1039/c7cp05139e

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