- values obtained at the MP2/aug-cc-pVQZ level of theory (S. Wang & Schaefer III, 2006);

isolated Ade, in the gas phase, is very flexible with a small degree of nonplanarity.

ν, cm-1

mol cm-1 kcal/

Base

∆∆G ∆∆<sup>E</sup>

0.02#

0.74#

0.03#

42.3\* 7.0#

318.6

28.9

Ade -0.06\* 0.12\*

Gua 0.37 0.91

Cyt 0.06 0.08

the C5-H group for Cyt

theory in vacuum

the equilibrium state (118.7°).

**3.2 Pyramidalization of the amine fragment of the Gua** 

Hovorun, 2010b);

adenine, which have no proton at the nitrogen atom located in the neighbourhood of the amino group. In guanine, one of the amino group hydrogen atoms oriented toward the N1- H bond is more bent down than the second amino group hydrogen atom oriented opposite to this bond. The amine fragment ≥C2-N2H2 (N1C2N2H=-31.1°; N3C2N2H=12.2°) of Gua can not be considered to be pyramidalized even at Т=0 К, since the zero-point vibrational energy associated with competent normal mode (542.6 cm-1), which frequency becomes imaginary (371.1 i cm-1) in the transition state of plane inversion, is higher than the planarization electronic energy barrier (0.91 kcal/mol or 318.6 cm-1).

The Gibbs free energies of activation of Gua interconversion *via* the plane-symmetric transition states TS2 and TS3 of the amino group rotation (5.40 and 9.14 kcal/mol) from its *trans*- and *cis*-orientation relative to the N1-C2 bond differ markedly from each other. Such a difference in Gibbs free energies of activation can be explained by the fact that the transition state TS2 is stabilized by electrostatic interactions of the LEP of the N2 atom with the hydrogen atom of the N1-H group and the amino group hydrogen atoms with the LEP of the N3 atom, while in the transition state TS3 these electrostatic interactions are displaced by repulsion of LEP of the N2 and N3 atom and the amino group hydrogen atoms from the N1- H group hydrogen atom that leads to destabilization of this transition state (Brovarets' and Hovorun, 2010b).

In the Gua\* mutagenic tautomer (ΔG=0.13 kcal/mol) which can mispair with Thy (Da̧bkowska et al., 2005; Danilov et al., 2005; Mejía-Mazariegos & Hernández-Trujillo, 2009) the hydroxyl group О6-Н is *cis*-oriented relatively to the N1-C6 bond. The barrier of planar inversion for Gua\* is significantly lower than that for Gua (Brovarets' & Hovorun, 2010b).

#### **3.3 Pyramidalization of the amine fragment of the Cyt**

We also demonstrated that Cyt is a structurally nonrigid molecule. Its interconversion occurs through three topologically and energetically distinct ways - plane inversion of the amine fragment ≥C4-N4H2 (N3C4N4H=7.2°; C5C4N4H=-11.7°) *via* the transition state TS1 and two anisotropic (clockwise and counterclockwise) rotations of the amino group around the exocyclic С4-N4 bond *via* the transition states TS2 and TS3, respectively. The planarization barrier of Cyt amino group is not large enough (28.9 cm-1) (Table 1) to allow the arrangement at least one vibrational level (n=0) of competent mode (212.1 cm-1), which frequency becomes imaginary (154.6 i cm-1) in the transition state TS1 of planarization of the Cyt amino group. The calculated low planarization barrier of Cyt leads to large amplitude anharmonic vibration of the amino group of Cyt over the barrier (Brovarets' and Hovorun, 2011a).

The Gibbs free energy of activation for rotation of the amino group about the C4-N4 bond when the LEP of the N4 atom is oriented to the hydrogen atom of the C5-H group (N3C4N4H1=56.6°; N3C4N4H2=-56.5°; HN4H=104.8°) is found to be notably lower (11.85 kcal/mol) than in the case when the LEP of the N4 atom is oriented to the N3 atom (N3C4N4H1=120.6°; N3C4N4H2=-120.6°; HN4H=107.4°) - 15.85 kcal/mol. This can be explained by the fact that the attractive interactions in the first case (the LEP of the N4 atom with the C5-H and amino protons with the LEP of the N3 atom) are replaced by repulsive ones (between the LEPs of the N4 and N3 atoms and between the amino protons and the hydrogen atom of the C5-H group).

Elementary Molecular Mechanisms of the Spontaneous Point

conjugation is purely quantum and has no classical analogue.

al., 2005, 2008; Dong & Miller, 2002).

**4.1 Mutagenic tautomers of DNA bases** 

**of their formation** 

biochemical significance.

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 69

2011a, 2011b, 2011c), is induced by anisotropic forces of crystal packaging and

The amine fragment ≥C-NH2 of DNA bases indeed determines their structural nonrigidity, which is in turn conditioned by quantum intramolecular effect, namely p-π-conjugation of a LEP of amino nitrogen atom with π-electron system of the ring. This specific phenomenon of

Exactly the structural nonrigidity of the polar amine fragment in DNA bases is a reason to adequately explain a static nonplanarity of amine fragment induced by an external electrical field which deforms it so that the projection of the induced dipole moment on the field direction is maximal and coincides with vector of field strength (Brauer et al., 2011; Choi et

**4. Mutagenic tautomers of DNA bases and possible molecular mechanisms** 

For structural chemists, rare tautomers of DNA bases are of special interest because they exert strong mutational pressures on the genome(Friedberg et al., 2006; Harris et al., 2003; Kwiatkowski & Pullman, 1975). That's why the tautomerism of DNA bases and their biologically active modifications (Kondratyuk et al., 2000; Samijlenko et al., 2001) have been the subject of a great number of theoretical and experimental investigations due to their

Numerous experimental and theoretical efforts have been directed towards the elucidation of qualitative and quantitative aspects of Cyt tautomerism, the data obtained up until about 1974 have been reviewed by Kwiatkowski and Pullman (Kwiatkowski & Pullman, 1975). In the solid phase, Cyt exists in a single keto-amino tautomeric state. However, experiments performed in the gas phase and in low-temperature inert matrices clearly demonstrated that Cyt exists as a mixture of several tautomeric forms (Bazsó et al., 2011; Brown et al., 1989b; Choi et al., 2005; Dong & Miller, 2002; Feyer et al., 2009; Govorun et al., 1992; Kostko et al., 2010; Lapinski et al., 2010; Min et al., 2009; Nir et al., 2001a, 2002a, 2002b; Nowak et al., 1989a; Radchenko et al., 1984; Szczesniak et al., 1988). Still, there are three matrix-isolation infrared spectroscopic studies on Cyt tautomerisation (Nowak et al., 1989a, 1989b; Radchenko et al., 1984; Szczesniak et al., 1988). Three tautomers of Cyt have been identified by molecular beam microwave spectroscopy with an estimated abundance of 1:1:0.25 for keto:amino-enol:keto-imino tautomers (Brown et al., 1989b). Several groups have explored the ultrafast excited-state dynamics of Cyt in molecular beams (Canuel et al., 2005; Kang et al., 2002; Kosma et al., 2009; Ullrich et al., 2004). As have been pointed out elsewhere (Fogarasi, 2002; Kosma et al., 2009; Ullrich, 2004), one ambiguity in these experiments is the

The first experimental observation of amino-keto and amino-enol tautomeric forms of Gua has been performed on isolated species in cold inert gas matrix by ground state infrared spectroscopy (Sheina et al., 1987; Szczepaniak & Szczesniak, 1987). By using UV–UV, IR–UV hole burning (Nir et al., 2001b, 2002b) and resonance-enhanced multiphoton ionization (REMPI) (Nir et al., 1999, 2002b) spectroscopy, de Vries and co-workers found spectral

coexistence of two or more tautomeric forms of Cyt in the gas phase.

intramolecular interactions within nucleosides or nucleotides, respectively.

So, extremely low planarization barrier implies that Ade, Cyt and Gua require very little energy to conform the structure of the amino group for formation of the complementary Hbonds with other molecules. This fact is very important for base pairing in nucleic acids or other polymers containing Ade, Gua and Cyt residues.

#### **3.4 Planarity or nonplanarity of DNA bases**

The thorough analysis of our results and also interpretation of the data reported in literature (Bludský et al., 1996; Hobza & Šponer, 1999; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Larsen et al., 1976; Lister et al., 1974; Šponer & Hobza, 1994; S. Wang & Schaefer III, 2006; Zierkiewicz et al., 2008) allow us to offer the following conclusions. The nucleobases with amino group are effectively planar structures with effective symmetry Cs. This is due to the fact that zero-point vibrational level of inverse out-of-plane vibration of their ≥C-NH2 amine fragment is located above the barrier of its plane inversion, and the maximum of the quadrate of the ψ-function for this vibration coincides with the barrier of the inversion (Fig. 1). In other words, the above-mentioned inversion oscillator has an essentially quantum behavior and can not be appropriately described in the framework of classical mechanics. "Equilibrium", "static" characteristics of the ≥C-NH2 amine fragment, namely the valence and dihedral angles, which are commonly interpreted by investigators as geometric parameters of equilibrium "nonplanarity" of amine fragment of Ade, Cyt and Gua, should be considered rather as dynamic characteristics of vibration mode of amine fragment inversion and no more than this.

At the same time, the two other nucleobases, Ura and Thy, are undoubtedly planar structures with point symmetry Cs (S. Wang & Schaefer III, 2006): the maximum of the quadrate of the ψ-function for low-frequency out-of-plane vibrations of pyrimidine ring coincides with the minimum of the potential energy that meets the planar structure (Fig. 1).

Fig. 1. Qualitative representation of potential energy profile (red line) of the amino group planarization in the case of Ade, Cyt and Gua (a) and out-of-plane ring deformation in the case of Ura and Thy (b) and quadrate of the ψ-function (blue line) for corresponding zeropoint vibrational levels

All canonical DNA bases are rather "soft" structures taking into account nonplanar out-ofplane deformation. Therefore, their static, equilibrium nonplanarity, which is observed, particularly in crystal state and in isolated nucleosides (Yurenko et al., 2007a, 2007b, 2007c, 2008, 2009; Zhurakivsky & Hovorun, 2006, 2007a, 2007b) or nucleotides (Nikolaienko et al., 2011a, 2011b, 2011c), is induced by anisotropic forces of crystal packaging and intramolecular interactions within nucleosides or nucleotides, respectively.

The amine fragment ≥C-NH2 of DNA bases indeed determines their structural nonrigidity, which is in turn conditioned by quantum intramolecular effect, namely p-π-conjugation of a LEP of amino nitrogen atom with π-electron system of the ring. This specific phenomenon of conjugation is purely quantum and has no classical analogue.

Exactly the structural nonrigidity of the polar amine fragment in DNA bases is a reason to adequately explain a static nonplanarity of amine fragment induced by an external electrical field which deforms it so that the projection of the induced dipole moment on the field direction is maximal and coincides with vector of field strength (Brauer et al., 2011; Choi et al., 2005, 2008; Dong & Miller, 2002).

#### **4. Mutagenic tautomers of DNA bases and possible molecular mechanisms of their formation**

#### **4.1 Mutagenic tautomers of DNA bases**

68 Quantum Chemistry – Molecules for Innovations

So, extremely low planarization barrier implies that Ade, Cyt and Gua require very little energy to conform the structure of the amino group for formation of the complementary Hbonds with other molecules. This fact is very important for base pairing in nucleic acids or

The thorough analysis of our results and also interpretation of the data reported in literature (Bludský et al., 1996; Hobza & Šponer, 1999; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Larsen et al., 1976; Lister et al., 1974; Šponer & Hobza, 1994; S. Wang & Schaefer III, 2006; Zierkiewicz et al., 2008) allow us to offer the following conclusions. The nucleobases with amino group are effectively planar structures with effective symmetry Cs. This is due to the fact that zero-point vibrational level of inverse out-of-plane vibration of their ≥C-NH2 amine fragment is located above the barrier of its plane inversion, and the maximum of the quadrate of the ψ-function for this vibration coincides with the barrier of the inversion (Fig. 1). In other words, the above-mentioned inversion oscillator has an essentially quantum behavior and can not be appropriately described in the framework of classical mechanics. "Equilibrium", "static" characteristics of the ≥C-NH2 amine fragment, namely the valence and dihedral angles, which are commonly interpreted by investigators as geometric parameters of equilibrium "nonplanarity" of amine fragment of Ade, Cyt and Gua, should be considered rather as dynamic characteristics of vibration mode of amine

At the same time, the two other nucleobases, Ura and Thy, are undoubtedly planar structures with point symmetry Cs (S. Wang & Schaefer III, 2006): the maximum of the quadrate of the ψ-function for low-frequency out-of-plane vibrations of pyrimidine ring coincides with the minimum of the potential energy that meets the planar structure (Fig. 1).

Fig. 1. Qualitative representation of potential energy profile (red line) of the amino group planarization in the case of Ade, Cyt and Gua (a) and out-of-plane ring deformation in the case of Ura and Thy (b) and quadrate of the ψ-function (blue line) for corresponding zero-

All canonical DNA bases are rather "soft" structures taking into account nonplanar out-ofplane deformation. Therefore, their static, equilibrium nonplanarity, which is observed, particularly in crystal state and in isolated nucleosides (Yurenko et al., 2007a, 2007b, 2007c, 2008, 2009; Zhurakivsky & Hovorun, 2006, 2007a, 2007b) or nucleotides (Nikolaienko et al.,

other polymers containing Ade, Gua and Cyt residues.

**3.4 Planarity or nonplanarity of DNA bases** 

fragment inversion and no more than this.

point vibrational levels

For structural chemists, rare tautomers of DNA bases are of special interest because they exert strong mutational pressures on the genome(Friedberg et al., 2006; Harris et al., 2003; Kwiatkowski & Pullman, 1975). That's why the tautomerism of DNA bases and their biologically active modifications (Kondratyuk et al., 2000; Samijlenko et al., 2001) have been the subject of a great number of theoretical and experimental investigations due to their biochemical significance.

Numerous experimental and theoretical efforts have been directed towards the elucidation of qualitative and quantitative aspects of Cyt tautomerism, the data obtained up until about 1974 have been reviewed by Kwiatkowski and Pullman (Kwiatkowski & Pullman, 1975). In the solid phase, Cyt exists in a single keto-amino tautomeric state. However, experiments performed in the gas phase and in low-temperature inert matrices clearly demonstrated that Cyt exists as a mixture of several tautomeric forms (Bazsó et al., 2011; Brown et al., 1989b; Choi et al., 2005; Dong & Miller, 2002; Feyer et al., 2009; Govorun et al., 1992; Kostko et al., 2010; Lapinski et al., 2010; Min et al., 2009; Nir et al., 2001a, 2002a, 2002b; Nowak et al., 1989a; Radchenko et al., 1984; Szczesniak et al., 1988). Still, there are three matrix-isolation infrared spectroscopic studies on Cyt tautomerisation (Nowak et al., 1989a, 1989b; Radchenko et al., 1984; Szczesniak et al., 1988). Three tautomers of Cyt have been identified by molecular beam microwave spectroscopy with an estimated abundance of 1:1:0.25 for keto:amino-enol:keto-imino tautomers (Brown et al., 1989b). Several groups have explored the ultrafast excited-state dynamics of Cyt in molecular beams (Canuel et al., 2005; Kang et al., 2002; Kosma et al., 2009; Ullrich et al., 2004). As have been pointed out elsewhere (Fogarasi, 2002; Kosma et al., 2009; Ullrich, 2004), one ambiguity in these experiments is the coexistence of two or more tautomeric forms of Cyt in the gas phase.

The first experimental observation of amino-keto and amino-enol tautomeric forms of Gua has been performed on isolated species in cold inert gas matrix by ground state infrared spectroscopy (Sheina et al., 1987; Szczepaniak & Szczesniak, 1987). By using UV–UV, IR–UV hole burning (Nir et al., 2001b, 2002b) and resonance-enhanced multiphoton ionization (REMPI) (Nir et al., 1999, 2002b) spectroscopy, de Vries and co-workers found spectral

Elementary Molecular Mechanisms of the Spontaneous Point

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 71

The existence of other Ade tautomers was evidenced by experimental studies (García-Terán et al., 2006; Gu & Leszczynski, 1999; Lührs et al., 2001; Stepanyugin et al., 2002a; Sukhanov et al., 2003), often in the presence of a metal (Samijlenko et al., 2004; Vrkic et al., 2004). It was also found that the Ade imino tautomer is more stabilized under the influence of

It is generally believed that Thy exists in the canonical diketo form in the gas phase as well as in the aqueous solution (Kwiatkowski & Pullman, 1975), but there is experimental evidence of small amounts of its rare tautomeric forms in the gas phase (Fujii et al., 1986; Tsuchiya et al., 1988) and in the solution (Hauswirth & Daniels, 1971; Katritzky & Waring, 1962; Morsy et al., 1999; Samijlenko et al., 2010; Suwaiyan et al., 1995). Also laser ablation in combination with MB-FTMW spectroscopy spectroscopy has been used to establish unambiguously the presence of the diketo form of thymine in the gas phase and to obtain its structure (López et al., 2007). In some theoretical reports, there is also a substantial emphasis on the energetic and structural characteristics of the stable isolated tautomers of Thy (Basu et al., 2005; Fan et al., 2010; Mejía-Mazariegos & Hernández-Trujillo, 2009), indicating that

In this section the intramolecular tautomerisation of nucleotide bases as a factor in spontaneous mutagenesis is considered using quantum-chemical calculation methods. In particular, the forward and reverse barrier heights for proton transfer reactions in isolated

The mutagenic tautomers of all DNA bases are depicted in Figure 2, while Table 2 shows their relative Gibbs free energies and kinetic parameters of the tautomerisation. As seen from Table 2 the mutagenic tautomers both of Cyt and Gua are energetically close to their

kcal/mol k, s-1 <sup>τ</sup>, s τ1/2, s τ99.9%, s

 # Δ∆GTS – the Gibbs free energy of activation for tautomerisation (T=298.15 K); k - the rate constant; τ – the lifetime; τ1/2 – the half-lifetime;; τ99.9% – the time necessary to reach 99.9% of the equilibrium concentration of rare tautomer in the system; ΔG – the relative Gibbs free energy of the tautomerized

Table 2. Basic thermodynamic and kinetic characteristics of intramolecular tautomerisation of DNA bases obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of

ΔG, kcal/mol <sup>K</sup>

5.141010 14.00 5.410-11

4.73107 11.64 2.88·10-9

1.351014 2.21 2.88·10-9

6.281010 0.13 7.98·10-1

charged platinum (Burda et al., 2000) or mercury (Zamora et al., 1997) cations.

the diketo is the most stable isomer both in the gas phase and in solution.

**4.2 Intramolecular tautomerisation of the DNA bases** 

Ade→Ade\* 45.58 9.6710-21 1.031020 7.171019

Ade\*→Ade 31.58 1.7910-10 5.59109 3.87109 Thy→Thy\* 39.09 5.6010-16 1.791015 1.241015

Thy\*→Thy 27.45 1.9510-7 5.14106 3.56106 Сyt→Сyt\* 38.47 1.6110-15 6.221014 4.311014

Сyt\*→Сyt 36.27 6.6810-14 1.501013 1.041013 Gua→Gua\* 32.17 6.5010-11 1.541010 1.071010

Gua\*→Gua 32.04 8.1510-11 1.231010 8.50109

base (T=298.15 K); К – the equilibrium constant of tautomerisation

DNA bases have been estimated and analysed.

Conversion Δ∆GTS,

theory in vacuum #

features that they assigned to the N9H keto, N7H keto, and N9H enol (*cis-* or *trans-*) forms. However, the most intense band assigned to the N9H enol was later attributed by Mons and co-workers (Chin et al., 2004; Mons et al., 2002) to a higher-energy form of the N7H enol tautomer. Furthermore, they observed the fourth band, which they assigned to the N9H *cis*enol form. Choi and Miller studied Gua molecules embedded in He droplets (Choi & Miller, 2006) and assigned the IR spectroscopic data to a mixture of the four more stable tautomeric forms: N7H keto, N9H keto, and N9H *cis-* and *trans-*enol. Mons et al. (Mons et al., 2006) later reported a new interpretation of the resonant two-photon ionization (R2PI) spectra. The authors suggested the occurrence of a fast nonradiative relaxation of the excited states of the N7H keto, N9H keto, and N9H *trans-*enol tautomeric forms that prevents the observation of these species in the R2PI spectra. The consistency between the experimental data obtained by molecular-beam Fourier-transform microwave (MB-FTMW) spectroscopy and theoretical calculations enabled Alonso and his collaborators to unequivocally identify the four most stable tautomers of guanine in the gas phase (Alonso et al., 2009). Recently also different tautomers of Gua were detected using vacuum ultraviolet (VUV) photoionization (Zhou et al., 2009). Theoretical calculations (Chen & Li, 2006; Elshakre, 2005; Hanus et al., 2003; Marian, 2007; Trygubenko et al., 2002) predict the existence of four low-energy tautomers with stabilities in the range 0–400 cm-1, whereby the keto tautomers with a hydrogen atom at the N7 or N9 atoms are the most stable.

Besides its role as a nucleic acid building block, Ade and its derivatives are of interest in various other biochemical processes. For example, it is the main component of the energystoring molecule adenosine triphosphate. Its high photostability under UV irradiation is an intriguing property that has been suggested to be essential for the preservation of genetic information (Crespo-Hernández et al., 2004).

Furthermore, the various tautomeric forms of Ade have been under substantial scrutiny (Hanus et al., 2004; Kwiatkowski & Leszczynski, 1992; Laxer et al., 2001; Mishra et al., 2000; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996; Plützer et al., 2001; Plützer & Kleinermanns, 2002; Salter & Chaban, 2002), because of their proposed role in mutagenic and carcinogenic processes (Danilov et al., 2005; Harris et al., 2003; Topal & Fresco, 1976). Some of the first IR spectra of Ade recorded in low-temperature inert gas matrices in the 400 to 4000 cm-1 range date back to 1985 (Stepanian et al., 1985). This study was extended by comparing the experimental spectra with calculated IR frequencies at different levels of theory (Brovarets' & Hovorun, 2011b; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996). It was concluded that the absorption of Ade was due to its 9H tautomer. Ade in the gas phase has been studied by UV photoelectron (Lin et al., 1980), microwave (Brown et al., 1989a), IR (Colarusso et al., 1997), jet-cooled REMPI (N.J. Kim et al., 2000; Lührs et al., 2001; Nir et al., 2001a, 2002b), IR–UV ion-dip (Nir et al., 2001a, 2002b; Plützer & Kleinermanns, 2002; Plützer et al., 2001; Van Zundert et al., 2011) and IR multiple-photon dissociation (IRMPD) spectroscopic investigations (Van Zundert et al., 2011). In all of these studies, it was suggested that the 9H amino tautomer of Ade is the dominant contributor to the spectra. The experimental results agree closely with calculations at different levels of theory and consistently show the 9H amino tautomer to be the most stable one (Brovarets' & Hovorun, 2011b; Hanus et al., 2004; Fonseca Guerra et al., 2006; Kwiatkowski & Leszczynski, 1992; Norinder, 1987; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996; Sabio et al., 1990; Saha et al., 2006; Sygula & Buda, 1983; Wiorkiewicz-Kuczera & Karplus, 1990).

features that they assigned to the N9H keto, N7H keto, and N9H enol (*cis-* or *trans-*) forms. However, the most intense band assigned to the N9H enol was later attributed by Mons and co-workers (Chin et al., 2004; Mons et al., 2002) to a higher-energy form of the N7H enol tautomer. Furthermore, they observed the fourth band, which they assigned to the N9H *cis*enol form. Choi and Miller studied Gua molecules embedded in He droplets (Choi & Miller, 2006) and assigned the IR spectroscopic data to a mixture of the four more stable tautomeric forms: N7H keto, N9H keto, and N9H *cis-* and *trans-*enol. Mons et al. (Mons et al., 2006) later reported a new interpretation of the resonant two-photon ionization (R2PI) spectra. The authors suggested the occurrence of a fast nonradiative relaxation of the excited states of the N7H keto, N9H keto, and N9H *trans-*enol tautomeric forms that prevents the observation of these species in the R2PI spectra. The consistency between the experimental data obtained by molecular-beam Fourier-transform microwave (MB-FTMW) spectroscopy and theoretical calculations enabled Alonso and his collaborators to unequivocally identify the four most stable tautomers of guanine in the gas phase (Alonso et al., 2009). Recently also different tautomers of Gua were detected using vacuum ultraviolet (VUV) photoionization (Zhou et al., 2009). Theoretical calculations (Chen & Li, 2006; Elshakre, 2005; Hanus et al., 2003; Marian, 2007; Trygubenko et al., 2002) predict the existence of four low-energy tautomers with stabilities in the range 0–400 cm-1, whereby the keto tautomers with a hydrogen atom

Besides its role as a nucleic acid building block, Ade and its derivatives are of interest in various other biochemical processes. For example, it is the main component of the energystoring molecule adenosine triphosphate. Its high photostability under UV irradiation is an intriguing property that has been suggested to be essential for the preservation of genetic

Furthermore, the various tautomeric forms of Ade have been under substantial scrutiny (Hanus et al., 2004; Kwiatkowski & Leszczynski, 1992; Laxer et al., 2001; Mishra et al., 2000; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996; Plützer et al., 2001; Plützer & Kleinermanns, 2002; Salter & Chaban, 2002), because of their proposed role in mutagenic and carcinogenic processes (Danilov et al., 2005; Harris et al., 2003; Topal & Fresco, 1976). Some of the first IR spectra of Ade recorded in low-temperature inert gas matrices in the 400 to 4000 cm-1 range date back to 1985 (Stepanian et al., 1985). This study was extended by comparing the experimental spectra with calculated IR frequencies at different levels of theory (Brovarets' & Hovorun, 2011b; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996). It was concluded that the absorption of Ade was due to its 9H tautomer. Ade in the gas phase has been studied by UV photoelectron (Lin et al., 1980), microwave (Brown et al., 1989a), IR (Colarusso et al., 1997), jet-cooled REMPI (N.J. Kim et al., 2000; Lührs et al., 2001; Nir et al., 2001a, 2002b), IR–UV ion-dip (Nir et al., 2001a, 2002b; Plützer & Kleinermanns, 2002; Plützer et al., 2001; Van Zundert et al., 2011) and IR multiple-photon dissociation (IRMPD) spectroscopic investigations (Van Zundert et al., 2011). In all of these studies, it was suggested that the 9H amino tautomer of Ade is the dominant contributor to the spectra. The experimental results agree closely with calculations at different levels of theory and consistently show the 9H amino tautomer to be the most stable one (Brovarets' & Hovorun, 2011b; Hanus et al., 2004; Fonseca Guerra et al., 2006; Kwiatkowski & Leszczynski, 1992; Norinder, 1987; Nowak et al., 1989b, 1991, 1994a, 1994b, 1996; Sabio et al., 1990; Saha et al., 2006; Sygula & Buda, 1983;

at the N7 or N9 atoms are the most stable.

information (Crespo-Hernández et al., 2004).

Wiorkiewicz-Kuczera & Karplus, 1990).

The existence of other Ade tautomers was evidenced by experimental studies (García-Terán et al., 2006; Gu & Leszczynski, 1999; Lührs et al., 2001; Stepanyugin et al., 2002a; Sukhanov et al., 2003), often in the presence of a metal (Samijlenko et al., 2004; Vrkic et al., 2004). It was also found that the Ade imino tautomer is more stabilized under the influence of charged platinum (Burda et al., 2000) or mercury (Zamora et al., 1997) cations.

It is generally believed that Thy exists in the canonical diketo form in the gas phase as well as in the aqueous solution (Kwiatkowski & Pullman, 1975), but there is experimental evidence of small amounts of its rare tautomeric forms in the gas phase (Fujii et al., 1986; Tsuchiya et al., 1988) and in the solution (Hauswirth & Daniels, 1971; Katritzky & Waring, 1962; Morsy et al., 1999; Samijlenko et al., 2010; Suwaiyan et al., 1995). Also laser ablation in combination with MB-FTMW spectroscopy spectroscopy has been used to establish unambiguously the presence of the diketo form of thymine in the gas phase and to obtain its structure (López et al., 2007). In some theoretical reports, there is also a substantial emphasis on the energetic and structural characteristics of the stable isolated tautomers of Thy (Basu et al., 2005; Fan et al., 2010; Mejía-Mazariegos & Hernández-Trujillo, 2009), indicating that the diketo is the most stable isomer both in the gas phase and in solution.

#### **4.2 Intramolecular tautomerisation of the DNA bases**

In this section the intramolecular tautomerisation of nucleotide bases as a factor in spontaneous mutagenesis is considered using quantum-chemical calculation methods. In particular, the forward and reverse barrier heights for proton transfer reactions in isolated DNA bases have been estimated and analysed.

The mutagenic tautomers of all DNA bases are depicted in Figure 2, while Table 2 shows their relative Gibbs free energies and kinetic parameters of the tautomerisation. As seen from Table 2 the mutagenic tautomers both of Cyt and Gua are energetically close to their


 # Δ∆GTS – the Gibbs free energy of activation for tautomerisation (T=298.15 K); k - the rate constant; τ – the lifetime; τ1/2 – the half-lifetime;; τ99.9% – the time necessary to reach 99.9% of the equilibrium concentration of rare tautomer in the system; ΔG – the relative Gibbs free energy of the tautomerized base (T=298.15 K); К – the equilibrium constant of tautomerisation

Table 2. Basic thermodynamic and kinetic characteristics of intramolecular tautomerisation of DNA bases obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory in vacuum #

Elementary Molecular Mechanisms of the Spontaneous Point

monomolecular (intramolecular) tautomerisation.

**4.3 The Löwdin's mechanism of the spontaneous point mutations** 

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 73

Of course, DNA bases are not isolated in living systems. In cellular DNA, the transition from canonical to mutagenic tautomers of nucleotide bases could be facilitated by the interactions with surrounding molecules. Also as suggested by Rodgers (Yang & Rodgers, 2004), bimolecular (intermolecular) tautomerisation may be much more feasible than

As seen from the literature survey, the possible tautomerisation of Gua·Cyt and Ade·Thy Watson-Crick base pairs occurs by Löwdin's mechanism (Fig. 3) through proton transfer along two neighbouring intermolecular H-bonds (Löwdin, 1963, 1965, 1966). However, the models exploring Löwdin's mechanism (Cerón-Carrasco et al., 2011; Cerón-Carrasco & Jacquemin, 2011; Florian et al., 1994, 1995; Florian & Leszczynski, 1996; Gorb et al., 2004; Villani, 2005, 2006, 2010) neglect the fact that electronic energy of reverse barriers of GuaCyt and AdeThy tautomerisation must exceed zero-point energy of vibrations causing this tautomerisation to provide dynamic stability (Gribov & Mushtakova, 1999) of the formed (Löwdin's) Gua\*・Cyt\* and Ade\*Thy\* mispairs, accordingly. In addition, this barrier must exceed a dissociation energy of the formed mispair to allow such complex easily dissociate into mutagenic tautomers during DNA replication. The results of our calculations definitely demonstrated that the zero-point energy 1475.9 and 1674.6 cm-1 (Table 7) for Gua\*・Cyt\* and Ade\*・Thy\* base pairs, accordingly, of corresponding vibrational modes which frequencies become imaginary in the transition states of Gua·Cyt and AdeThy base pairs tautomerisation lies above (1800.8 cm-1) and under (37.7 cm-1) the value of the reverse barrier, accordingly (Table 3, 7). This means that Ade\*·Thy\* mispair is

Fig. 3. Interconversion of Ade·Thy↔Ade\*·Thy\* and Gua·Cyt↔Gua\*·Cyt\* base pairs resulting from the mutagenic tautomerisation of DNA bases. Relative Gibbs free (T=298.15 K, in

311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory and reported near each structure in kcal/mol. The dotted lines indicate H-bonds AH…B (their lengths H…B are presented in

vacuum) and electronic (in brackets) energies are obtained at the MP2/6-

angstroms), while continuous lines show covalent bonds

canonical tautomers that is in a complete agreement with the experimental data on Cyt and Gua tautomers (Nir et al., 1999, 2001a, 2001b, 2002a, 2002b) and their Gibbs free energy differences are only 2.21 and 0.13 kcal/mol, relatively. The considerably greater differences in energy of 14 and 12 kcal/mol were found for the mutagenic tautomers of Ade and Thy, respectively. This finding can explain why the mutagenic tautomers of Ade and Thy can not be detected experimentally.

Fig. 2. Intramolecular tautomerisation of the DNA bases. The dotted line indicates intramolecular H-bond N1H…O6 in TS4, while continuous lines show covalent bonds. Relative Gibbs free energy is presented near each structure in kcal/mol (T=298.15 K, in vacuum)

The intramolecular proton transfer schemes for isolated DNA bases are displayed in Figure 2. The MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) reaction barriers for the forward tautomerisation are 45.58 (Ade), 39.09 (Thy), 38.47 (Cyt) and 32.17 kcal/mol (Gua) and these values tightly correlate with the literature data (Basu et al., 2005; Brovarets' & Hovorun, 2010a, 2010f; Danilov et al., 2005; Fan et al., 2010; Fogarasi & Szalay, 2002; Fogarasi, 2008; Fonseca Guerra et al., 2006; Gorb & Leszczynski, 1998a, 1998b; Gorb et al., 2001; Gu & Leszczynski, 1999; Hanus et al., 2003, 2004; Kosenkov et al., 2009; Mejía-Mazariegos & Hernández-Trujillo, 2009; Saha et al., 2006). Very large kinetic barriers for intramolecular tautomerisation of all isolated DNA bases (above 32 kcal/mol) indicate that such tautomerisation will be very slow and this process may not occur readily in the isolated molecule. So, in such a way it is not possible to attain the equilibrium concentrations within biologically important period of time, namely during the replication of one base pair (*ca.* 10-4 s), as the value of *τ*99.9% amounts to more than 107 s. However, mutagenic tautomers, once formed, will be stable with a lifetime that by 3–10 orders exceeds the typical time of DNA replication in the cell (~103 s). This fact confirms that the postulate, on which the Watson-Crick tautomeric hypothesis of spontaneous transitions grounds, is adequate (Brovarets' & Hovorun, 2010a). It should be noted that equilibrium constants of Ade (5.410-11) and Thy (2.8810-9) tautomerisation fall within the range of measured mutation frequency, but for the Cyt (2.410-2) and Gua (8.010-1) - remain above this value.

canonical tautomers that is in a complete agreement with the experimental data on Cyt and Gua tautomers (Nir et al., 1999, 2001a, 2001b, 2002a, 2002b) and their Gibbs free energy differences are only 2.21 and 0.13 kcal/mol, relatively. The considerably greater differences in energy of 14 and 12 kcal/mol were found for the mutagenic tautomers of Ade and Thy, respectively. This finding can explain why the mutagenic tautomers of Ade and Thy can not

Fig. 2. Intramolecular tautomerisation of the DNA bases. The dotted line indicates

Cyt (2.410-2) and Gua (8.010-1) - remain above this value.

intramolecular H-bond N1H…O6 in TS4, while continuous lines show covalent bonds. Relative Gibbs free energy is presented near each structure in kcal/mol (T=298.15 K, in vacuum)

The intramolecular proton transfer schemes for isolated DNA bases are displayed in Figure 2. The MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) reaction barriers for the forward tautomerisation are 45.58 (Ade), 39.09 (Thy), 38.47 (Cyt) and 32.17 kcal/mol (Gua) and these values tightly correlate with the literature data (Basu et al., 2005; Brovarets' & Hovorun, 2010a, 2010f; Danilov et al., 2005; Fan et al., 2010; Fogarasi & Szalay, 2002; Fogarasi, 2008; Fonseca Guerra et al., 2006; Gorb & Leszczynski, 1998a, 1998b; Gorb et al., 2001; Gu & Leszczynski, 1999; Hanus et al., 2003, 2004; Kosenkov et al., 2009; Mejía-Mazariegos & Hernández-Trujillo, 2009; Saha et al., 2006). Very large kinetic barriers for intramolecular tautomerisation of all isolated DNA bases (above 32 kcal/mol) indicate that such tautomerisation will be very slow and this process may not occur readily in the isolated molecule. So, in such a way it is not possible to attain the equilibrium concentrations within biologically important period of time, namely during the replication of one base pair (*ca.* 10-4 s), as the value of *τ*99.9% amounts to more than 107 s. However, mutagenic tautomers, once formed, will be stable with a lifetime that by 3–10 orders exceeds the typical time of DNA replication in the cell (~103 s). This fact confirms that the postulate, on which the Watson-Crick tautomeric hypothesis of spontaneous transitions grounds, is adequate (Brovarets' & Hovorun, 2010a). It should be noted that equilibrium constants of Ade (5.410-11) and Thy (2.8810-9) tautomerisation fall within the range of measured mutation frequency, but for the

be detected experimentally.

Of course, DNA bases are not isolated in living systems. In cellular DNA, the transition from canonical to mutagenic tautomers of nucleotide bases could be facilitated by the interactions with surrounding molecules. Also as suggested by Rodgers (Yang & Rodgers, 2004), bimolecular (intermolecular) tautomerisation may be much more feasible than monomolecular (intramolecular) tautomerisation.

#### **4.3 The Löwdin's mechanism of the spontaneous point mutations**

As seen from the literature survey, the possible tautomerisation of Gua·Cyt and Ade·Thy Watson-Crick base pairs occurs by Löwdin's mechanism (Fig. 3) through proton transfer along two neighbouring intermolecular H-bonds (Löwdin, 1963, 1965, 1966). However, the models exploring Löwdin's mechanism (Cerón-Carrasco et al., 2011; Cerón-Carrasco & Jacquemin, 2011; Florian et al., 1994, 1995; Florian & Leszczynski, 1996; Gorb et al., 2004; Villani, 2005, 2006, 2010) neglect the fact that electronic energy of reverse barriers of GuaCyt and AdeThy tautomerisation must exceed zero-point energy of vibrations causing this tautomerisation to provide dynamic stability (Gribov & Mushtakova, 1999) of the formed (Löwdin's) Gua\*・Cyt\* and Ade\*Thy\* mispairs, accordingly. In addition, this barrier must exceed a dissociation energy of the formed mispair to allow such complex easily dissociate into mutagenic tautomers during DNA replication. The results of our calculations definitely demonstrated that the zero-point energy 1475.9 and 1674.6 cm-1 (Table 7) for Gua\*・Cyt\* and Ade\*・Thy\* base pairs, accordingly, of corresponding vibrational modes which frequencies become imaginary in the transition states of Gua·Cyt and AdeThy base pairs tautomerisation lies above (1800.8 cm-1) and under (37.7 cm-1) the value of the reverse barrier, accordingly (Table 3, 7). This means that Ade\*·Thy\* mispair is

Fig. 3. Interconversion of Ade·Thy↔Ade\*·Thy\* and Gua·Cyt↔Gua\*·Cyt\* base pairs resulting from the mutagenic tautomerisation of DNA bases. Relative Gibbs free (T=298.15 K, in vacuum) and electronic (in brackets) energies are obtained at the MP2/6- 311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory and reported near each structure in kcal/mol. The dotted lines indicate H-bonds AH…B (their lengths H…B are presented in angstroms), while continuous lines show covalent bonds

Elementary Molecular Mechanisms of the Spontaneous Point

the nucleic acid bases through H-bonds (López et al., 2010).

including the Wigner's tunnelling correction (Wigner, 1932).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 75

microwave spectroscopy (López et al., 2010). Investigation of the structure of the adducts from the rotational constants of the different isotopologues shows that the observed conformers of bases correspond to the most stable forms in which water closes a cycle with

In this work we for the first time present a complete study of the proton transfer kinetic of intramolecular water-assisted tautomerisation mechanism for all DNA bases (Fig. 4) by computing the rate constants with the conventional transition state theory (Atkins, 1998),

Fig. 4. Water-assisted tautomerisation of the DNA bases. The dotted lines indicate H-bonds AH…B (their lengths H…B are presented in angstroms), while continuous lines show covalent bonds. Relative Gibbs free energies (T=298.15 K, in vacuum) are obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory and reported near each

We found that the interaction of the canonical tautomers of the DNA bases with a water molecule at the Watson-Crick edge changes the gas-phase stability: the relative Gibbs free energies of the Ade and Thy decrease, while those of the Cyt and Gua – increase (Table 4). So, it means that in the case of complexes with water, the order of stability of Ade and Thy mutagenic tautomers remains the same as for isolated bases; moreover, they are stabilized in these complexes. On the contrary, the order of stability of Cyt and Gua mutagenic tautomers

structure in kcal/mol

dynamically unstable, moreover, the value of its reverse barrier (in terms of Gibbs free energy) is negative (-1.01 kcal/mol) indicating that Ade\*·Thy\* minimum completely disappears from the Gibbs free energy surface. Therefore, Ade\*·Thy\* mispair really doesn't exist (Fig. 3). By comparing the values of zero-point energy (Table 3, 7) and the reverse barrier (Tables 3, 7) of the Gua·Cyt↔Gua\*·Cyt\* tautomerisation, we came to the conclusion that Gua\*·Cyt\* mispair is metastable.

