The Radical Cationic Repair Pathway of Cyclobutane Pyrimidine Dimer: The Effect of Sugar-Phosphate Backbone

Abstract

Radical cationic repair process of cis–syn thymine dimer has been investigated when (1) sugar-phosphate backbones were substituted by hydrogen atoms, (2) phosphate group was substituted by two hydrogen atoms each on a sugar ring and (3) sugar-phosphate backbone was taken into account. The effect of the interactions between N1 and N1′ lone pairs and the C6-C6′ antibonding orbital are the most important evidences for the cleavage of the C6-C6′ bond in the first step of radical cationic repair mechanism in the absence of the sugar-phosphate backbone. The impact of the N1 and N1′ lone pairs on the C6-C6′ bond cleavage decreases and the energy barrier of the cleavage of that bond significantly increases in the presence of the deoxynucleoside sugars and the sugar-phosphate backbone.

Introduction

Interaction of DNA and RNA bases with ultraviolet light (UV) leads to the formation of cyclobutane pyrimidine dimers (CPDs), such as thymine and uracil dimers, between two adjacent pyrimidine bases on a DNA or RNA strand [1, 2]. The formation of a thymine cyclobutane dimer in a DNA strand is also possible by DNA-photosensitizers [3]. Some of these are increasingly used as antibiotics to treat a broad range of bacterial infections [4]. A major photoproduct is the cis–syn pyrimidine dimer [5, 6] that is formed by [2 + 2] cycloaddition [7-9]. These lesions are harmful to living cells; they have mutagenic (inhibit the DNA transcription and replication; [10, 11]), carcinogenic (skin cancers; [12]) and cytotoxic [13] effects on cellular systems.

In nature, pyrimidine dimers are repaired via enzymatic systems. Photoreactivation of the lesions is possible by DNA photolyase enzymes [14-17], which utilize light of wavelengths between 360 and 460 nm (near-UV and visible light) to initiate the cycloreversion reaction. Splitting of CPDs is carried out by electron transfer from or to the dimer [18, 19]. Photoreduction and photo-oxidation of the pyrimidine dimer occur, respectively, in the presence of anion and cation radicals in the repair pathway. Experimental studies on several model systems including photoreducing and photo-oxidizing sensitizers have showed that the cycloreversion of CPDs can alternatively occur via radical cationic and radical anionic repair pathways [20]. Thermodynamical investigations [10, 19, 21] and kinetic isotope effect studies [22, 23] suggest that the fragmentation (by direct reduction of CPDs) is operative in the biological systems when FADH⁻ (contains a reduced deprotonated flavin) is present in the enzyme structure [24].

The repair of pyrimidine dimers can also be carried out chemically [25]. Chemical sensitizers can repair the dimer by either electron donation to the dimer (radical anion formation) or electron acceptation from the dimer (radical cation formation; [26]). Anthraquinone derivatives are among the sensitizers which are activated by light and repair the cis–syn pyrimidine dimers by one electron oxidation [27]. Furthermore, thymine dimers can also be repaired in a reaction involving DNA-mediated electron transfer that is photoactivated after irradiation at 400 nm [28].

Photorepair of pyrimidine dimers has so far been investigated from both experimental [6, 29-33] and theoretical [1, 34-42] points of view. The most popular studies include the DNA photolyase enzyme and radical anionic repair pathway [10, 33, 43-53]. Some experimental [28] and theoretical [9, 39-42] studies, including molecular dynamic simulations and static ab initio calculations, have previously been carried out on radical cationic mechanism.

As shown in Scheme 1, the C5-C5′ and C6-C6′ bonds are present between two thymine monomers. In all previous studies [39-42], stepwise mechanism starting with the cleavage of the C6-C6′ bond was suggested for the radical cationic repair of CPD. In the present work, the radical cationic repair mechanism of thymine dimer has been considered with three models of the cis–syn thymine dimer to characterize the role of the sugar backbone on the repair mechanism in the presence and absence of the phosphate bridge using quantum mechanical calculations, for the first time. Why is the repair of the dimer triggered by the C6-C6′ cleavage in the radical cationic pathway and followed by the C5-C5′ cleavage? How can the sugar backbone affect the profile energy surface along the repair pathway in the presence and absence of the phosphate bridge? Answering these questions are the fundamental challenges in this work. The study of electronic and steric effects as well as the charge and spin distribution on different moieties of the cis–syn thymine dimer along the repair pathway makes it possible to understand easily the repair mechanism.

Scheme 1. Atom numbering: a, b, and c correspond to the first, second and third model of cis–syn thymine dimer, respectively.

Methods

The most abundant pyrimidine dimer, the cis–syn thymine dimer, has been chosen for the computational study on the details of the radical cationic repair pathway. As can be seen in Scheme 1, the sugar-phosphate backbones are replaced with hydrogen atoms, and with the sugar rings in two models of the cis–syn thymine dimer.

It has previously been reported [42] that the MP2 method is not suitable for the prediction of the radical cationic repair pathway because of well-known problems in treating spin contaminated open-shell species. In addition, it has been reported [42] that the hybrid Hartree Fock density functional theory B3LYP method is unable to locate the transition state for the second bond cleavage. Therefore, UHF, complete active space self-consistent field CASSCF and higher method CCSD and CCSD(T) calculations were employed to predict the radical cationic pathway. All the calculations were carried out using the Gaussian09 [54] program package. Along the repair path, UHF wave functions were checked for spin contamination. <S²> values did not exceed 0.81 and 0.75 before and after annihilation, respectively. Thus, these calculations are nearly free of spin contamination. Single-point calculations were performed on transition state and ground state structures obtained at the UHF/6-31G(d) level by the CASSCF(3e,4o)/6-31G(d,p) level of theory for all models, and the CCSD/6-31G and the CCSD(T)/6-31G(d,p) levels of theory for the first model of cis–syn thymine dimer to compare the energy barriers of the C6-C6′ and C5-C5′ cleavage at several levels of theory. All stationary points were checked by frequency calculation at the UHF/6-31G(d) level of theory. All frequencies were positive for reactants and intermediate, while only one imaginary frequency was obtained for transition state structures that were also checked by the movement described by the eigenvector associated with the imaginary frequency. In addition, the intrinsic reaction co-ordinate (IRC) calculations verified the transition states in the smallest model.

To determine the special characters of the structures obtained in the repair process, population analysis was performed by the natural bond orbital (NBO; [55]) and the atoms in molecules (AIM; [56]) methods on the wave functions obtained at the UHF/6-31G(d) level of theory by NBO3.1 [57] and AIM2000 [58] programs. To discuss the charge distribution on the A and B thymine rings (see Scheme 1) in the repair mechanism, atomic net charges were calculated using the ChelpG schemes [59]. The Mulliken spin density [60] was computed at the UHF/631G(d) level of theory. We employed Mulliken spin population analyses which are believed to be reliable for our system as the spin density values are in agreement with the trend of radical cationic repair mechanism.

Results and Discussion

cis–syn thymine dimer in the absence of the sugar-phosphate backbone

Stationary point structures including neutral cis–syn thymine dimer (T<>T), thymine dimer radical cation (T<>T(∙+)), transition states (TS1 and TS2), intermediate (INT), and products (PC1 and PC2) have been considered along the radical cationic cycloreversion of the thymine dimer. The removal of an electron from T<>T produces T<>T(∙+) which leads to INT via TS1. Subsequently, INT leads to PC1 by TS2. PC1 and PC2 are cationic and neutral repaired structures, respectively. PC2 is obtained when one electron is absorbed by PC1. T<>T(∙+), TS1, INT, TS2 and PC1 are cationic and T<>T and PC2 are neutral among the stationary point structures along the repair pathway.

Stationary point structures and schematic profile energy calculated at the different levels of theory are illustrated in the first model of the thymine dimer in Fig. 1. The choice of an appropriate computational method for the radical ions is crucial for the validity of the obtained results. As can be seen in Fig. 1, two transition states that correspond to the C6-C6′ and the C5-C5′ bond cleavage are observed at the UHF/6-31G(d) and CASSCF(3,4)/6-31G(d,p) levels, while one transition state is observed at the CCSD/6-31G and CCSD(T)/6-31G(d,p) levels of theory (see Fig. 1). CCSD is a nonvariational method, while other methods are variational. This may affect the energy barrier difference between the CCSD method and others.

Figure 1. Stationary point structures and the ΔE₁ (energy barrier of the C6-C6′ bond cleavage in kcal mol⁻¹) and ΔE₂ (energy barrier of the C5-C5′ bond cleavage) values along the reaction path in the first model of the dimer at the CASSCF(3,4)/6-31G(d,p) level of theory. From top to bottom, numbers correspond to the UHF/6-31G(d), CASSCF(3,4)/6-31G(d,p), CCSD/6-31G and CCSD(T)/6-31G(d,p) levels of theory.

The bond length of C6-C6′/C5-C5′ changes from 1.570/1.593 Å in T<>T to 2.090/1.587 Å in T<>T(∙+). As can be seen in Table 1, weakening of the C6-C6′ bond is accompanied with an increase in the occupation number of the σ*_C6C6′ orbital and a decrease in the occupation number of the σ_C6C6′ orbital. This is followed by TS1, so that the C6-C6′ bond cleavage is completed in the INT structure. The evidences for the weakening of C5-C5′ bond are observed in the TS2 structure. Therefore, the TS1 and TS2 structures correspond to the C6-C6′ and C5-C5′ cleavages, respectively.

Table 1. The occupancies of the most important σ and σ* orbitals and the occupation numbers of the most important lp orbitals (in au) in the stationary point structures

	T<>T	T<>T(∙+)	TS1	INT	TS2	PC1	PC2
^†Italicized values correspond to the σ* antibonding orbitals; ^‡the values in second line correspond to the π and π* orbitals.
C6-C6′	1.974, 0.041^†	0.977, 0.111	0.973, 0.133
C5-C5′	1.953, 0.031	1.945, 0.035	1.946, 0.036	1.945, 0.047	1.772, 0.192
N1-C6	1.989, 0.022	1.989, 0.015 ^‡0.957,0.040	1.989, 0.015 0.965, 0.036	1.990, 0.014 1.954, 0.063	1.989, 0.014 0.972, 0.047	1.987, 0.015	1.987, 0.016
C5-C6	1.970, 0.024	1.972, 0.024	1.972, 0.024	1.974, 0.024	1.976, 0.020	1.979, 0.018 1.862, 0.149	1.980, 0.018 1.882, 0.138
C4-O4	1.995, 0.012 1.990, 0.170	1.995, 0.008 1.989, 0.158	1.995, 0.007 1.990, 0.153	1.995, 0.007 1.990, 0.141	1.995, 0.008 1.987, 0.162	1.995, 0.009	1.995, 0.009 1.989, 0.245
N1′-C6′	1.986, 0.018	1.989, 0.015 0.958, 0.038	1.990, 0.014 0.955, 0.032	1.989, 0.012	1.988, 0.013	1.990, 0.013 0.959, 0.014	1.986, 0.016
C5′-C6′	1.978, 0.063	1.971, 0.022	1.972, 0.020	1.976, 0.018	1.979, 0.017	1.982, 0.017 0.942, 0.105	1.980, 0.018 1.887, 0.141
C4′-O4′	1.995, 0.009 1.990, 0.166	1.994, 0.011 0.994, 0.069	1.994, 0.010 0.994, 0.074	1.995, 0.010 1.990, 0.178	1.995, 0.009 1.985, 0.184	1.995, 0.007 0.968, 0.050	1.995, 0.008 1.989, 0.225
C4′-N3′	1.989, 0.063	1.988, 0.071 0.934, 0.279	1.988, 0.069 0.938, 0.272	1.989, 0.063	1.988, 0.064	1.988, 0.068	1.988, 0.069
N1	1.798	0.887	0.861		0.804	1.716	1.730
N1′	1.809	0.896	0.905	1.753	1.718	0.867	1.715
N3′	1.737	0.865	0.864	1.725	1.719	1.723	1.724
O4	1.976, 1.893	1.975, 1.879	1.975, 1.877	1.975, 1.875	1.976, 1.880	1.973, 1.909, 1.610	1.968, 1.899
O4′	1.977, 1.895	1.976, 1.877, 0.715	1.975, 1.879, 0.723	1.974, 1.886	1.976, 1.884	1.979, 1.888, 0.817	1.977, 1.893
C6′				0.958	0.818

Why is the cleavage of the C6-C6′ bond easier and faster than the C5-C5′ bond in the radical cationic pathway of the first model of the cis–syn thymine dimer (see Fig. 1)? There are two evidences. First, two electron-withdrawing groups (CO) are in the vicinity of the C5-C5′ bond, so the removal of an electron from the σ_C5C5′ orbital is more difficult than the σ_C6C6′ orbital. Second, on the basis of NBO analysis, the most important evidence for the beginning of the repair by the cleavage of the C6-C6′ bond is the effect of the interactions between N1 and N1′ lone pairs and the C6-C6′ antibonding orbital (the lp_N1 and lp_N1′ effects). The increase in the donor-acceptor lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions increases the occupation number of the σ*_C6C6′ orbital that leads to the weakening of the C6-C6′ bond. According to Table 1, the occupation number of the σ*_C6C6′ orbital increases in the T<>T(∙+) and TS1 structures. The ChelpG charges on the N1 and N1′ atoms decrease from −0.78 and −0.75e to −0.65 and −0.72e along the T<>T(∙+) formation, respectively, which are in agreement with the interaction of the N1 lone pair (lp_N1) and the N1′ lone pair (lp_N1′) with the σ*_C6C6′ orbital.

The most important interactions, in which the σ*_C5C5′ and σ*_C6C6′ orbitals act as acceptor, are gathered in Table 2. The interactions which weaken the C6-C6′ bond are stronger than those that weaken the C5-C5′ bond in all structures from T<>T to TS1, such that the C6-C6′ bond cleavage is easier than C5-C5′. In the T<>T, T<>T(∙+) and TS1 structures, energy of the σ_C7H7(3) → σ*_C5C5′ and σ_{C7′H7′(3)} → σ*_C5C5′ interactions is lower than 6.0 kcal mol⁻¹, while energy of the lp_N1′ → σ*_C6C6′ and lp_N1 → σ*_C6C6′ interactions is significantly higher than 6.0 kcal mol⁻¹. The energies of interactions, in which the σ*_C5C5′ acts as acceptor, are approximately identical in the T<>T, T<>T(∙+) and TS1 structures. But the increase in the lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interaction energies is impressive from the T<>T to T<>T(∙+) structure. As can be seen in Table 2, the lp_N1′ → σ*_C6C6′ interaction energy decreases and the lp_N1 → σ*_C6C6′ interaction energy increases from the T<>T(∙+) to the TS1 structure. In the INT and TS2 structures, a new interaction with the σ*_C5C5′ acceptor is observed with an energy higher than 7.0 kcal mol⁻¹. In the TS2 structure, the energies of interactions with the σ*_C5C5′ acceptor becomes higher than 40.0 kcal mol⁻¹ (45.75 kcal mol⁻¹ for the lp_C6′ → σ*_C5C5′ interaction).

Table 2. E⁽²⁾ values (in kcal mol⁻¹) of the most important interactions in the stationary point structures

	E ^(2)
	T<>T	T<>T(∙+)	TS1	INT	TS2
Italicized and bold values correspond to the second and third model, respectively. *and ^†correspond to the lp(1)C6′ → σ*(1)C5C5′ and lp(1)C6 → σ*(1)C5C5′ interactions, respectively.
lpN1′ → σ*(1)C6C6′	6.92, 14.62, 14.54	23.54, 5.45, 9.27	14.21, 7.79, 16.41
lpN1 → σ*(1) C6C6′	15.44, 6.82, 11.58	29.71, 8.69, 4.21	49.44, 13.18, 6.61	7.44*, 7.54^†, 10.02*	45.75*, 55.69^†, 17.63*
σ C7H7(3) → σ*(1) C5C5′	5.66, 5.24, 5.60	5.49, 5.78, 5.61	5.16, 2.85, 5.53	4.57, 5.73, 4.05	6.43, 7.49, 4.68
σC7′H7′(3) → σ*(1)C5C5′	5.30, 5.50, 5.68	5.76, 5.46, 6.01	5.80, 5.45, 5.88	5.75, 4.52, 5.42	7.49, 6.52, 6.80
lpN1′ → σ*(1)C1″C2″	8.44, 8.02	2.18, 4.13	2.13, 3.63	2.87	1.89
lpN1′ → σ*(2) C2′O2′	87.76, 61.60	41.26	38.66	32.41	33.50
lpN1 → σ*(2)C2O2	68.84, 76.1	52.38	58.10	62.28	63.57
lpN1 → σ*(1) C1′C2′	3.86, 5.24	2.75, 1.62	2.91, 1.67	3.04	3.50
lpN1 → σ*(1)C1′O1′	14.46, 14.06	13.58, 3.59	13.33, 3.54	13.73	12.16
lpN1′ → σ*(1)C1″O1″	1.38, 11.7	4.28	4.67	7.63	8.25
lp(1)O1′ → σ*(1)N1C1′	1.62, 1.08	1.94, 1.35	1.96, 1.33	1.78, 1.26	1.86, 1.26
lp(2)O1′ → σ*(1)N1C1′	7.08, 7.44	6.87, 9.68	7.11, 9.96	7.96, 10.59	8.81, 10.59
lp(1)O1″ → σ*(1)N1′C1″	0.78, 1.98	0.30, 1.37	0.30, 1.54	1.22	1.69
lp(2)O1″ → σ*(1)N1′C1″	10.1, 3.36	17.82, 5.22	17.7, 5.15	17.83, 2.69	15.87, 2.00

The C6-C6′ bond cleavage (in the INT structure) leads to changes in the dimer structure and makes cleavage of the C5-C5′ bond easier. According to Table 2, cleavage of the C5-C5′ bond is extremely affected by the lone pair on the C6′ atom (lp_C6′), which is made along the C6-C6′ bond cleavage in the INT structure via the lp_C6′ → σ*_C5C5′ interaction.

Role of the deoxynucleoside sugar and the sugar-phosphate backbone

As shown in Figs. 2 and 3, the energy barrier of the C6-C6′ (and C5-C5′) bond cleavage changes significantly in the presence of deoxynucleoside sugar rings and the sugar-phosphate backbone. The full optimization of T<>T(∙+) in the second model of T<>T reveals that the C6-C6′ bond is weaker than C5-C5′, such that the bond length of C6-C6′/C5-C5′ in the second model changes from 1.558/1.572 Å in the T<>T to 1.583/1.575 Å in the T<>T(∙+) structure. So, the repair process of the dimer in the second model is also started by the relaxed scan of the C6-C6′ bond and followed by C5-C5′. The energy barrier of the C6-C6′ (and C5-C5′) bond cleavage increases at the UHF/6-31G(d) and CASSCF(3e,4o)/6-31G(d,p) levels of theory (see Fig. 2). The energy barrier of the C6-C6′/C5-C5′ bond cleavage is 1.29/7.97 and 14.75/9.49 kcal mol⁻¹ at the UHF/6-31G(d) and CASSCF/6-31G(d,p) levels of theory, respectively. With respect to structural parameters, intramolecular interactions in T<>T(.+) are expected to be higher than in TS1. Much of the difference between ΔE1 values calculated at the UHF/6-31G(d) and CASSCF/6-31G(d,p) levels may be attributed to the underestimation of these interactions at the former level.

Figure 2. Stationary point structures and the ΔE₁ and ΔE₂ (in kcal mol⁻¹) values along the reaction pathway in the presence of sugar rings. From top to bottom, numbers correspond to the UHF/6-31G(d) and CASSCF(3,4)/6-31G(d,p) levels of theory.

Figure 3. Stationary point structures and the ΔE₁ and ΔE₂ (in kcal mol⁻¹) values along the reaction pathway in the presence of the sugar-phosphate backbone. From top to bottom, numbers correspond to the UHF/6-31G(d) and CASSCF(3,4) method in conjunction with the 6-31G and 6-31G(d,p) basis sets.

As the energy barrier of the C5-C5′ bond cleavage is lower than that of C6-C6′ through the CASSCF method, the repair pathway of the dimer has been started with the relaxed scan of the C5-C5′ bond and followed by C6-C6′. In this case, the energy barrier of the C5-C5′/C6-C6′ bond cleavage is calculated to be 40.40/1.44 and 47.28/19.93 kcal mol⁻¹ at the UHF/6-31G(d) and CASSCF/6-31G(d,p) levels of theory, respectively. Therefore, the C5-C5′ bond cleavage is more difficult than C6-C6′ at the first step. This conclusion is also confirmed by the NBO analysis. The C6-C6′ bond cleavage, at the first step, is accompanied by the strong donor–acceptor lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions, whereas these or other similar interactions which can facilitate the bond cleavage are not provided for the C5-C5′ bond cleavage. In addition, steric effects can be part of the factors that drive the outcome of the reaction. The opening of the C5-C5′ bond, at the first step, causes steric hindrance around the sugar rings that prevents the chemical reaction.

Figure 3 shows the stationary point structures and schematic profile energy calculated at the different levels of theory along the repair pathway in the presence of the sugar-phosphate backbone. In the presence of the sugar-phosphate backbone, the cleavage of the C6-C6′ bond occurs without the energy barrier, while the barrier for the C5-C5′ bond cleavage is equal to 10.44 kcal mol⁻¹ at the UHF/6-31G(d) level of theory. The full optimization of T<>T(∙+) in the presence of the sugar-phosphate backbone reveals that the bond length of the C6-C6′/C5-C5′ bond changes from 1.564/1.587 and 1.566/1.596 Å in the T<>T to 2.881/1.596 and 1.574/1.597 Å in the T<>T(∙+) structure at the UHF/6-31G(d) and CASSCF(3,4)/6-31G levels of theory, respectively. Indeed, the repair process of the dimer in the third model has also been investigated by the relaxed scan of C6-C6′ and then the C5-C5′ bond at the CASSCF(3,4)/6-31G level of theory.

As shown in Table 2, the donor–acceptor interactions of the lone pair orbitals of N1 and N1′ atoms with the sugar rings are substantially stronger than the lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions in the T<>T, T<>T(∙+) and TS1 structures. The lp_N1′ → σ*_C2′O2′ and lp_N1 → σ*_C2O2 interactions are also notable in these structures. The overlap of lone pair orbitals of the N1 and N1′ atoms with the antibonding orbitals of the C1″-C2″, C1′-C2′, C1′-O1′, C1″-O2″, C2′-O2′ and C2-O2 bonds is possible in the optimized structure of T<>T in the second and third models. The overlapping of the lone pair orbitals of N1 and N1′ atoms with the antibonding orbital of the C6-C6′ bond decreases in the presence of those strong interactions. The decrease in the lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions increases the energy barrier of the C6-C6′ bond cleavage. So, the decrease in the impact of lp_N1 and lp_N1′ effects on the cleavage of the C6-C6′ bond is a result of the presence of the sugar ring in the dimer structure.

After the cleavage of the C6-C6′ bond in the INT structure, the lp_C6 → σ*_C5C5′ and lp_C6′ → σ*_C5C5′ interactions can efficiently facilitate the cleavage of the C5-C5′ bond. The lp_C6 and lp_C6′ orbitals are formed as a result of the C6-C6′ bond cleavage.

The sum of the donor–acceptor interaction energies (ΣE²) was calculated for those interactions in which σ*_C5C5′ and σ*_C6C6′ orbitals act as acceptors. These values are equal to 26.6/36.3 and 83.3/41.74 kcal mol⁻¹ for TS1 and TS2 in the second/third model. Thus, the cleavage of the C5-C5′ bond in the TS2 structure is easier than C6-C6′ in the TS1 structure. The energy barriers calculated by the CASSCF method for the cleavage of C6-C6′ and C5-C5′ bonds in the presence of sugar rings and the sugar-phosphate backbone are in agreement with the population analyses data. So, the CASSCF method gives more reasonable results than UHF in the presence of deoxynucleoside sugar rings and the sugar-phosphate backbone in the dimer structure.

The role of sugar rings on C6-C6′ and C5-C5′ bond cleavage is identical in the absence and presence of the phosphate group, such that the energy barriers increase along the reaction path. But, the increase in the energy barriers is more significant in the absence of the phosphate group. This can be related to the electronic effects of the phosphate group. This group contains four electronegative oxygen atoms that can affect the charge transfer on different moieties of the dimer and thereby control the rate of reaction.

The electron and spin densities and the charge distribution

In the absence of the sugar-phosphate backbone

As can be seen in Table 3, the sum of the calculated ChelpG atomic charges of T<>T are positive and negative on the thymine rings A and B (see Scheme 1), respectively. The positive charge is distributed on both the A and B rings after T<>T(∙+) formation. In addition to the weakening of the C6-C6′ bond in the T<>T(∙+) structure, the spin density on ring B becomes greater than that on A (see Table 4). Ring A becomes more positive than B because the electron density of the C6-C6′ bond is further transferred to ring B rather than A. These changes continue, such that the spin density values become close to zero and 1e⁻ on rings A and B, respectively, in the INT. Thus, the unpaired electron is mostly localized on ring B of the thymine dimer in the INT structure. The electron affinity of ring A is greatly enhanced on the basis of the ChelpG positive charges calculated on ring A. This is a result of nonuniform cleavage of the C6-C6′ bond, which is followed by nonuniform cleavage of the C5-C5′ bond.

Table 3. ChelpG charges on different moieties of dimer for the stationary point structures

	A	B	A′	B′	Phos.
Bold and italicized values correspond to the second and third model, respectively.
T<>T	0.043, −0.268, −0.232	−0.043, −0.247, −0.271	0.242, 0.628	0.273, 0.574	− 0.699
T<>T(∙+)	0.590, −0.085, 0.435	0.410, 0.385, −0.063	0.308, 0.647	0.392, 0.584	− 0.603
TS1	0.704, −0.052, 0.414	0.296, 0.361, −0.026	0.312, 0.622	0.261, 0.598	− 0.609
INT	0.867, −0.165, 0.452	0.133, 0.455, −0.030	0.285, 0.686	0.425, 0.494	− 0.603
TS2	0.691, 0.048, 0.433	0.309, 0.270, −0.034	0.252, 0.703	0.429, 0.516	− 0.620
PC1	0.053, −0.206, 0.655	0.946, 0.510, −0.210	0.249, 0.656	0.447, 0.568	− 0.670
PC2	0.037, −0.221, −0.231	−0.037, −0.277, −0.280	0.219, 0.591	0.279, 0.518	− 0.597

Table 4. Mulliken spin densities (×10) on different moieties of the stationary point structures

	A	B	A′	B′	Phos. group
Bold and italicized values correspond to the second and third model, respectively.
T<>T(∙+)	4.84, 1.14, 9.59	5.16, 9.13, 0.84	0.01, −0.45	−0.27, 0.00	0.00
TS1	3.31, 2.30, 8.22	6.69, 7.97, 2.20	0.00, −0.42	−0.26, −0.00	0.00
INT	0.55, 9.47, 0.68	9.45, 0.56, 9.24	−0.03, −0.00	0.00, 0.07	0.00
TS2	3.64, 5.85, 1.63	6.36, 4.27, 8.34	−0.09, −0.01	−0.03, 0.04	0.00
PC1	0.03, 0.02, 10.17	9.97, 10.14, 0.00	0.00, −0.18	−0.16, 0.00	0.00

The electron density of this bond is transferred more to ring A rather than B upon TS2 formation. So, the ChelpG charges calculated on ring A/B become more negative/positive relative to the INT structure (see Table 3). Despite increasing/decreasing spin density of ring A/B, spin density of ring B is greater than that of A (see Table 4).

Both the ChelpG charges and the spin densities are close to zero and 1e⁻ in ring A and B, respectively, in the PC1 structure. As ring A is more positive than B in the TS2 structure, the electron density of the C5-C5′ bond is further transferred to ring A on PC1 formation. The electron deficiency is completely compensated on ring A, and is enhanced on ring B, such that the unpaired electron is mostly localized on ring B of the thymine dimer in the PC1 structure. Therefore, the C5-C5′ bond cleavage is also nonuniform. Finally, one electron is absorbed by ring B in the PC2 structure to obtain the neutralized system.

In the presence of the deoxynucleoside sugars

Positive charge is mostly localized on rings A′, B′ and B (see Scheme 1b and c) in the T<>T(∙+) species (see Table 3). The highest value of spin density indicates that the unpaired electron is localized on ring B. Thus, the electron charge transfer from the C6-C6′ bond to ring B is higher than A upon the weakening of that bond in the TS1 structure. The charge transfer from ring B to B′ accompanies the electron deficiency on ring B′. Consequently, the probability of the presence of unpaired electron (correspond to spin density values) decreases on rings B and B′.

After the C6-C6′ bond cleavage, the spin density values are close to 1e⁻ on ring A and are very small on ring B. So, the unpaired electron is mostly localized on ring A in the INT formation. During the C6-C6′ bond cleavage the electron charge transfer from the C6-C6′ bond to ring A is different from B. Therefore, the cleavage of the C6-C6′ bond is also nonuniform in the presence of the deoxynucleoside sugar.

Ring B has a high tendency to pull the electron density of the C5-C5′ bond on passing the TS2 structure because B is the most positive ring in the INT structure. The electron charge transfer from the C5-C5′ bond to ring A is lower than B, such that the spin density decreases/increases substantially on ring A/B, respectively (see Table 4).

The maximum value of the spin density corresponds to ring B upon PC1 formation (see Table 4). The positive charge on ring B is higher than A in the TS2 structure, so, the electron charge transfer from the C5-C5′ bond to ring B is more appropriate than A along PC1 formation, which leads to a nonuniform cleavage of the C5-C5′ bond. AIM analysis reveals that the electron charge transfer from ring B to A (interaction between O4 atom of A and N1′ atom of B) is such that ring B becomes more positive with a higher spin density than A in the PC1 structure (see Table 4). Finally, repaired thymine dimer is obtained by one electron donation to system upon PC2 formation.

In the presence of the sugar-phosphate backbone

The electron oxidation process reinforces the charge transfer from the sugar-phosphate backbone to the thymine rings in the T<>T(∙+) structure. With respect to the charge values and spin densities, the unpaired electron is probably localized on ring A in the T<>T(∙+) structure. The spin density is transferred from ring A to B along the weakening of the C6-C6′ bond on passing the TS1 structure. On the basis of the increases/decreases in the ChelpG charges of ring A/A′ (and B/B′), the electron charge transfer from ring A to A′ (and from ring B to B′) compensates the electron deficiency of ring A′ (and B′); however, A′ is maintained as the most positive ring in the TS1 structure. Because of the low electron density transfer from the C6-C6′ bond to ring B in the TS1 structure, the spin density increases on ring B (see Table 4). The spin density of the unpaired electron is localized on ring B in the INT structure (up to 0.924e⁻). With the cleavage of the C6-C6′ bond upon INT formation, the electron charge density is transferred to ring A (because of the positive/negative charge on ring A/B). Also, the charge transfer from ring A to A′ compensates some of the electron deficiency on ring A′. Therefore, the spin density becomes close to zero on the mentioned rings. According to the above discussion, a nonuniform cleavage is expected for the C6-C6′ bond.

As can be seen in Table 3, ring A is more positive than B in the INT structure. So, the electron charge transfer from the C5-C5′ bond to ring A is higher than B upon weakening the C5-C5′ bond in the TS2 structure. The spin density distribution on the TS2 structure indicates that the electron density of the unpaired electron is fully localized far from the sugar-phosphate backbone (see Table 4).

The spin density becomes close to 1e⁻ on ring A and significantly drops on the other moieties in the dimer structure upon PC1 formation. The electron density of the C5-C5′ bond is completely transferred to ring A and the process is followed by the electron transfer from ring A to A′ to compensate the electron deficiency on ring A′, which is a result of nonuniform cleavage of the C5-C5′ bond. The electron deficiency on ring B is compensated via the charge transfer from ring B′ to B. One electron donation to PC1 structure neutralizes the system, and two thymine monomers are restored upon PC2 formation.

Conclusions

In the absence of the sugar-phosphate backbone, the cleavage of the C6-C6′ bond is strongly affected by the lp_N1 and lp_N1′ effects (lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions) in the first step of the repair pathway, while this effect or other similar effects are not observed for the cleavage of the C5-C5′ bond. Thus, the cleavage of C6-C6′ is easier and faster than the C5-C5′ bond. The cleavage of the C6-C6′ bond leads to the formation of lp_C6′ that contributes to the elongation of the C5-C5′ bond via the lp_C6′ → σ*_C5C5′ interaction in the TS2 structure.

The CASSCF results obtained in the presence of deoxynucleoside sugar rings and the sugar-phosphate backbone are different from those obtained for Model 1. The energy barrier of the C6-C6′ bond cleavage calculated by the CASSCF(3,4) method is several times higher than that of C5-C5′. The lp_N1 and lp_N1′ orbitals have important roles along the repair pathway. The interactions of lp_N1 and lp_N1′ with the antibonding orbitals of sugar rings are more significant than the lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions along the reaction pathway. The energies of the lp_N1 → σ*_C6C6′ and lp_N1′ → σ*_C6C6′ interactions decrease and thereby the energy barrier of the C6-C6′ cleavage increases in the presence of both sugar rings and the sugar-phosphate backbone. The increase in the energy barrier of the C6-C6′ and C5-C5′ bonds with the sugar rings is higher than that in the absence of the phosphate group.

The steric hindrance around the sugar rings prevents the cleavage of the C5-C5′ bond before the C6-C6′ bond cleavage along the repair pathway in the presence of sugar rings.

The charge, and the electron and spin density distribution on the moieties obtained along the repair mechanism indicate that both the C6-C6′ and C5-C5′ bond cleavages are nonuniform in the three studied models of the cis–syn thymine dimer.