**Elementary Molecular Mechanisms of the Spontaneous Point Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding**

Ol'ha O. Brovarets'1,2,3, Iryna M. Kolomiets'1 and Dmytro M. Hovorun1,2,3 *1Department of Molecular and Quantum Biophysics, Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, Kyiv, 2Research and Educational Center "State Key Laboratory of Molecular and Cell Biology", Kyiv, 3Department of Molecular Biology, Biotechnology and Biophysics, Institute of High Technologies, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine* 

## **1. Introduction**

58 Quantum Chemistry – Molecules for Innovations

Sherman, L.; Edelstein, F.; Shtacher, G.; Avramoff, M. & Teitz, Y. (1980). Inhibition of Moloney

Stevens, W.J.; Basch, H. & Krauss, M. (1984). Compact effective potentials and efficient

*Gen. Virol*., Vol. 46, No. 1, pp. (195-203), ISSN: 0022-1317.

81, No. 12, pp. (6026-6033), ISSN: 0021-9606.

Leukaemia Virus Production by *N*-methylisatin-β-4′:4′-diethylthiosemicarbazone. *J.* 

shared‐exponent basis sets for the first‐ and second‐row atoms. *J. Chem. Phys.,* Vol.

DNA replication is an amazing biological phenomenon that is essential to the continuation of life (Kornberg & Baker, 1992). Faithful replication of DNA molecules by DNA polymerases is essential for genome integrity and stable transmission of genetic information in all living organisms. Although DNA replicates with immensely high fidelity, upon assembly of millions of nucleotides a DNA polymerase can make mistakes that are a major source of DNA mismatches. The overall accuracy and error spectrum of a DNA polymerase are determined mainly by three parameters: the nucleotide selectivity of its active site, its mismatch extension capacity, and its proofreading ability (Beard & Wilson, 1998, 2003; Joyce & Benkovic, 2004). Yet, natural and exogenous sources of DNA damage result in a variety of DNA modications, the most common including nucleobase oxidation (Nakabeppu et al., 2007), alkylation (Drabløs et al., 2004) and deamination (Ehrlich et al., 1986; Kow, 2002; Labet et al., 2008).

Depending on the type of mismatch and the biological context of its occurrence, cells must apply appropriate strategies of postreplication repair to avoid mutation (Kunz et al., 2009). However, some replication errors make it past these mechanisms, thus becoming permanent mutations after the next cell division.

Mutations are stable, heritable alterations of the genetic material, namely DNA (Friedberg et al., 2006). They are an important contributor to human aging, metabolic and degenerative disorders, cancer, and cause heritable diseases, at the same time they are the kindling factor for biological evolution of living things. Beyond the individual level, perhaps the most dramatic effect of mutation relates to its role in evolution; indeed, without mutation,

Elementary Molecular Mechanisms of the Spontaneous Point

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 61

and positioned in sheared relative to the Watson-Crick configuration represent erroneous occurrences leading to the substitution mutations. The wobble mispairings were observed in X-ray (Brown et al., 1985; Hunter et al., 1986; Kennard, 1985) and NMR (Patel et al., 1982a, 1982b, 1984a, 1984b) model experiments (in the absence of DNA polymerases) on cocrystallization of complementary oligonucleotides containing a single mismatched base pair. But such experimental conditions do not properly reflect those required for enzymatic DNA replication (Kornberg & Baker, 1992). The GuaThy and Ade·Cyt mismatches adopt a relatively stable and well-fitting wobble configurations, supporting intrahelical base pair stacking and affecting the DNA helical structure only marginally (Brown et al., 1985; Kunz et al., 2009). By structural considerations, mispairings that cause little distortion to the canonical Watson-Crick geometry are more likely to be tolerated by the polymerase active site and, therefore, to escape proofreading. This fact was demonstrated in structural and biochemical studies of DNA polymerases (Echols & Goodman, 1991; Kool, 2002). However, enzymes, involved in postreplication repair, can easily recognize and correct structural

imperfections between such improperly paired nucleotides (Kunz et al., 2009).

Another mechanism of the spontaneously arising point mutations in DNA was originally proposed by James Watson and Francis Crick (Watson & Crick, 1953a, 1953b) and further elaborated by Topal and Fresco (Topal & Fresco, 1976) as the "rare tautomer hypothesis" which suggested that "spontaneous mutation may be due to a base occasionally occurring in one of its less likely tautomeric forms". Both the purine and pyrimidine bases in DNA exist in different chemical forms, so-called isomers or tautomers, in which the protons occupy different positions in the molecule. Tautomers of DNA bases – Ade, Gua, Thy and Cyt - can cause genetic mutations by pairing incorrectly with wrong complementary bases. Watson and Crick suggested two possible transition mispairs, Gua·Thy and Ade·Cyt, involving the enol form of guanine or thymine and the imino form of adenine or cytosine, respectively – Gua\*·Thy, Gua·Thy\*, Ade\*·Cyt and Ade·Cyt\* (herein and after mutagenic tautomeric forms of bases are marked by an asterisk). These mispairs fit well within the dimensions of the DNA double helix to preserve the geometry of a correct canonical base pair in such a way supporting the Watson and Crick's original idea that spontaneous base substitutions, namely transition mutations, may result from mismatches shaped like correct base pairs, which were experimentally confirmed by Bebenek et al. for DNA polymerase λ (Bebenek et al., 2011) and by Wang et al. for DNA polymerase I (W. Wang et al., 2011). However, it remains out of eyeshot whether these rare (or mutagenic) tautomers are dynamically stable and their lifetimes are long enough to cause mutations or they are short-lived structures unable to yield irreversible errors in DNA and finally induce genomic alterations. The actual lifetime was estimated only for mutagenic tautomer of Cyt, with a value being about 600 years (Zhao et al., 2006). But evidence for these types of tautomeric shifts remains sparse, because the limited sensitivity of the experimental methods prevents an accurate detection of the relative amount of the rare tautomers including mutagenic. Among all rare tautomers, only the imino tautomers of Cyt (Brown et al., 1989b; Dreyfus et al., 1976; Feyer et al., 2010; Szczesniak et al., 1988) and enol tautomers of Gua (Choi & Miller, 2006; Sheina et al., 1987; Plekan et al., 2009; Szczepaniak & Szczesniak, 1987) were experimentally detected. The lack of the experimental data on the rare tautomers of Ade (Brown et al., 1989a) and Thy can be explained by the high value of their relative energy (~12÷14 kcal/mol at 298.15 K) estimated by theoretical investigations (Basu et al., 2005; Brovarets' & Hovorun, 2010a; Fonseca Guerra et al., 2006; Mejía-Mazariegos & Hernández-Trujillo, 2009; Samijlenko et al., 2000, 2004).

evolution would not be possible. The point mutations caused by the substitution of one nucleotide base for another are divided into *transitions* (replacement of a purine with another purine or replacement of a pyrimidine with another pyrimidine, i.e. purinepyrimidine mismatches) and *transversions* (replacement of a purine with a pyrimidine or *vice versa*, i.e. purine-purine and pyrimidine-pyrimidine mispairs). Therefore, to maintain a stable genome, it is essential for cells to monitor the state of base pairing in their genomes and to correct mismatches that will occasionally occur.

Spontaneous mutations are generally occurring due to endogenous factors: endogenous chemical lesions generated during normal cell metabolism, errors in normal cellular processes and others.

It has been suggested that there are two major approaches to the origin of mutations arising during DNA replication:


There is a natural — albeit low — error rate that occurs during DNA replication. So, the average frequency of spontaneous errors in DNA replication is in the range of 10-8÷10-11 per base pair replicated per one cell division (Drake, 1991; Fersht & Knill-Jones, 1983; Loeb, 2001).

Nowadays the occurrence of the spontaneous point mutations can be explained by several physico-chemical mechanisms.

Today, scientists generally consider that most DNA replication errors are caused by mispairings with "correct" geometry formed either by the protonated or deprotonated bases (i.e., bases with an excess or missing proton, respectively) (Sowers et al., 1986, 1987; Yu et al., 1993), which generation and existence under physiological conditions remains disputable, because it was claimed that the methods used by researchers to determine ionized base pairing involve conditions different from those actually obtained during DNA replication. So, Bebenek et al. (Bebenek et al., 2011) demonstrated that wild-type DNA polymerase λ and its derivative polymerase λ DL misinsert dGTP opposite template Thy at substantially higher efficiencies in reactions performed at pH 9.0 as compared to those at physiological pH (7.0). These pH dependencies of enzymatic catalysis are in agreement with the results of Yu et al. (Yu et al., 1993) and are also consistent with the possible involvement of an ionized base pair. However, in our recent work (Brovarets' et al., 2010e), it was demonstrated that the ionization mechanism of spontaneous transitions appearance does not imply any advantages in comparison with other mechanisms described in literature. Moreover, we revealed that the protonation/deprotonation of base in any canonical nucleoside significantly perturbs its DNA-like conformations (Brovarets' et al., 2010e).

It is also generally accepted in the literature that wobble base pairs (Gua·Thy and Ade·Cyt) (Brown et al., 1985; Crick, 1966; Hunter et al., 1986; Kennard, 1985; Padermshoke et al., 2008; Patel et al., 1982a, 1982b, 1984a, 1984b) formed by bases in their canonical tautomeric forms

evolution would not be possible. The point mutations caused by the substitution of one nucleotide base for another are divided into *transitions* (replacement of a purine with another purine or replacement of a pyrimidine with another pyrimidine, i.e. purinepyrimidine mismatches) and *transversions* (replacement of a purine with a pyrimidine or *vice versa*, i.e. purine-purine and pyrimidine-pyrimidine mispairs). Therefore, to maintain a stable genome, it is essential for cells to monitor the state of base pairing in their genomes

Spontaneous mutations are generally occurring due to endogenous factors: endogenous chemical lesions generated during normal cell metabolism, errors in normal cellular

It has been suggested that there are two major approaches to the origin of mutations arising

1. *replication errors*, that occur due to mispair formation in the DNA double helix as a result of changing the coding property (for example, tautomeric) of DNA base in the

2. *incorporation errors*, that occur due to mispair formation in the DNA double helix as a result of changing the coding property (for example, tautomeric) of DNA base in the

There is a natural — albeit low — error rate that occurs during DNA replication. So, the average frequency of spontaneous errors in DNA replication is in the range of 10-8÷10-11 per base pair replicated per one cell division (Drake, 1991; Fersht & Knill-Jones, 1983; Loeb, 2001). Nowadays the occurrence of the spontaneous point mutations can be explained by several

Today, scientists generally consider that most DNA replication errors are caused by mispairings with "correct" geometry formed either by the protonated or deprotonated bases (i.e., bases with an excess or missing proton, respectively) (Sowers et al., 1986, 1987; Yu et al., 1993), which generation and existence under physiological conditions remains disputable, because it was claimed that the methods used by researchers to determine ionized base pairing involve conditions different from those actually obtained during DNA replication. So, Bebenek et al. (Bebenek et al., 2011) demonstrated that wild-type DNA polymerase λ and its derivative polymerase λ DL misinsert dGTP opposite template Thy at substantially higher efficiencies in reactions performed at pH 9.0 as compared to those at physiological pH (7.0). These pH dependencies of enzymatic catalysis are in agreement with the results of Yu et al. (Yu et al., 1993) and are also consistent with the possible involvement of an ionized base pair. However, in our recent work (Brovarets' et al., 2010e), it was demonstrated that the ionization mechanism of spontaneous transitions appearance does not imply any advantages in comparison with other mechanisms described in literature. Moreover, we revealed that the protonation/deprotonation of base in any canonical nucleoside

It is also generally accepted in the literature that wobble base pairs (Gua·Thy and Ade·Cyt) (Brown et al., 1985; Crick, 1966; Hunter et al., 1986; Kennard, 1985; Padermshoke et al., 2008; Patel et al., 1982a, 1982b, 1984a, 1984b) formed by bases in their canonical tautomeric forms

significantly perturbs its DNA-like conformations (Brovarets' et al., 2010e).

and to correct mismatches that will occasionally occur.

incoming deoxyribonucleoside triphosphate.

processes and others.

during DNA replication:

template strand;

physico-chemical mechanisms.

and positioned in sheared relative to the Watson-Crick configuration represent erroneous occurrences leading to the substitution mutations. The wobble mispairings were observed in X-ray (Brown et al., 1985; Hunter et al., 1986; Kennard, 1985) and NMR (Patel et al., 1982a, 1982b, 1984a, 1984b) model experiments (in the absence of DNA polymerases) on cocrystallization of complementary oligonucleotides containing a single mismatched base pair. But such experimental conditions do not properly reflect those required for enzymatic DNA replication (Kornberg & Baker, 1992). The GuaThy and Ade·Cyt mismatches adopt a relatively stable and well-fitting wobble configurations, supporting intrahelical base pair stacking and affecting the DNA helical structure only marginally (Brown et al., 1985; Kunz et al., 2009). By structural considerations, mispairings that cause little distortion to the canonical Watson-Crick geometry are more likely to be tolerated by the polymerase active site and, therefore, to escape proofreading. This fact was demonstrated in structural and biochemical studies of DNA polymerases (Echols & Goodman, 1991; Kool, 2002). However, enzymes, involved in postreplication repair, can easily recognize and correct structural imperfections between such improperly paired nucleotides (Kunz et al., 2009).

Another mechanism of the spontaneously arising point mutations in DNA was originally proposed by James Watson and Francis Crick (Watson & Crick, 1953a, 1953b) and further elaborated by Topal and Fresco (Topal & Fresco, 1976) as the "rare tautomer hypothesis" which suggested that "spontaneous mutation may be due to a base occasionally occurring in one of its less likely tautomeric forms". Both the purine and pyrimidine bases in DNA exist in different chemical forms, so-called isomers or tautomers, in which the protons occupy different positions in the molecule. Tautomers of DNA bases – Ade, Gua, Thy and Cyt - can cause genetic mutations by pairing incorrectly with wrong complementary bases. Watson and Crick suggested two possible transition mispairs, Gua·Thy and Ade·Cyt, involving the enol form of guanine or thymine and the imino form of adenine or cytosine, respectively – Gua\*·Thy, Gua·Thy\*, Ade\*·Cyt and Ade·Cyt\* (herein and after mutagenic tautomeric forms of bases are marked by an asterisk). These mispairs fit well within the dimensions of the DNA double helix to preserve the geometry of a correct canonical base pair in such a way supporting the Watson and Crick's original idea that spontaneous base substitutions, namely transition mutations, may result from mismatches shaped like correct base pairs, which were experimentally confirmed by Bebenek et al. for DNA polymerase λ (Bebenek et al., 2011) and by Wang et al. for DNA polymerase I (W. Wang et al., 2011). However, it remains out of eyeshot whether these rare (or mutagenic) tautomers are dynamically stable and their lifetimes are long enough to cause mutations or they are short-lived structures unable to yield irreversible errors in DNA and finally induce genomic alterations. The actual lifetime was estimated only for mutagenic tautomer of Cyt, with a value being about 600 years (Zhao et al., 2006). But evidence for these types of tautomeric shifts remains sparse, because the limited sensitivity of the experimental methods prevents an accurate detection of the relative amount of the rare tautomers including mutagenic. Among all rare tautomers, only the imino tautomers of Cyt (Brown et al., 1989b; Dreyfus et al., 1976; Feyer et al., 2010; Szczesniak et al., 1988) and enol tautomers of Gua (Choi & Miller, 2006; Sheina et al., 1987; Plekan et al., 2009; Szczepaniak & Szczesniak, 1987) were experimentally detected. The lack of the experimental data on the rare tautomers of Ade (Brown et al., 1989a) and Thy can be explained by the high value of their relative energy (~12÷14 kcal/mol at 298.15 K) estimated by theoretical investigations (Basu et al., 2005; Brovarets' & Hovorun, 2010a; Fonseca Guerra et al., 2006; Mejía-Mazariegos & Hernández-Trujillo, 2009; Samijlenko et al., 2000, 2004).

Elementary Molecular Mechanisms of the Spontaneous Point

**2. Computational methods** 

potential energy landscape.

311++G(d,p) geometries.

reactions.

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 63

molecular and structural approaches to the nature of spontaneous DNA mutations caused by prototropic tautomerism of nucleotide bases and to provide a novel quantum-chemical

The *ab initio* methods were used to investigate the tautomerisation of the DNA bases and mispairs involving mutagenic tautomers. All quantum-chemical calculations were

Geometries and harmonic vibrational frequencies of molecules and complexes were obtained using Becke's three-parameter exchange functional (B3) (Becke, 1993) combined with Lee, Yang, and Parr's (LYP) correlation functional (Lee et al., 1988) implemented in Gaussian 03 that has good performance for calculating barrier heights, thermo-chemical kinetics or intra- and intermolecular H-bonds in the systems recently studied (Brovarets', 2010; Brovarets' & Hovorun, 2010a, 2010b, 2010d, 2010f, 2011a, 2011b; Brovarets' et al., 2010c, 2010e) and 6-311++G(d,p) basis set. The absence of imaginary vibrational frequencies proved that energy-minimized structures perfectly correspond to the local minima of the

To consider electronic correlation effects as accurately as possible, we performed single point energy calculations at the MP2/6-311++G(2df,pd) level of theory for the B3LYP/6-

As for the transition states (TS) of tautomerisation of the isolated bases or their complexes, they were located by means of Synchronous Transit-guided Quasi-Newton (STQN) method (Peng & Schlegel, 1993; Peng et al., 1996) using the Berny algorithm and proved to contain one and only one imaginary frequency corresponding to the reaction coordinate. Afterwards the reaction pathway of proton transfer was followed by performing an intrinsic reaction coordinate calculation in order to make sure that transition state really connects the expected reactants and products (Gonzalez & Schlegel, 1989). We applied the standard transition state theory (Atkins, 1998) to estimate barriers for tautomerisation

The equilibrium constants of tautomerisation were calculated using the standard equation K=exp(-ΔG/RT), where ΔG is the relative Gibbs free energy of the reactant or product, T is

The time τ99.9% necessary to reach 99.9% of the equilibrium concentration of the mutagenic tautomer in the system of reversible first-order forward (k*f*) and reverse (k*r*) reactions (canonical

3

(1)

10 *f r ln k k*

↔ mutagenic tautomer transitions) can be estimated from the equation (Atkins, 1998)

99.9%

tunneling effects are accounted by the Wigner's tunnelling correction (Wigner, 1932).

and the lifetime τ and the half-lifetime τ1/2 of the complexes are given by 1/k and ln(2)/k, respectively. We applied the standard transition state theory (Atkins, 1998) in which quantum

the absolute temperature, and R is the universal gas constant.

insight into the classical understanding of this biologically important problem.

performed using the Gaussian 03 program package (Frisch et al., 2003).

Unusual tautomeric forms of modified bases have been found in damaged DNA duplex, indicating that the transition to such altered forms is indeed feasible (Chatake et al., 1999; Robinson et al., 1998). It is therefore likely that analogues of DNA bases have a propensity to adopt the rare, namely mutagenic tautomeric forms (Brovarets' & Hovorun, 2010b, 2011a).

The molecular nature of formation of mutagenic tautomers is not quite clear yet. Several alternative mechanisms of the rare tautomers formation have been discussed in the literature: i) intramolecular proton transfer in DNA bases (Basu et al., 2005; Brovarets' & Hovorun, 2010a, 2010d, 2011a; Gorb et al., 2005; Zhao et al., 2006), ii) proton transfer in a single base assisted by bulk aqueous solution, by micro-hydration or by a single interacting water molecule (Fogarasi, 2008; Furmanchuk et al., 2011; Gorb & Leszczynski, 1998a, 1998b; H.-S. Kim et al., 2007; Michalkova et al., 2008); iii) Löwdin's mechanism of tautomerisation involving double proton transfer (DPT) along two intermolecular hydrogen (H) bonds of complementary DNA base pairs (Löwdin, 1963, 1965, 1966).

On the basis of the Watson-Crick's model Löwdin (Löwdin, 1963, 1965, 1966) suggested that spontaneous mutagenesis causing aging and cancer could be induced by tautomerisation of Ade・Thy and Gua・Cyt Watson-Crick base pairs through DPT along neighbouring intermolecular H-bonds joining bases in pairs. Following the pioneering Löwdin's work the DNA base pairs have been extensively studied using a wide range of theoretical approaches, essentially in the gas phase (Cerón-Carrasco et al., 2011a; Cerón-Carrasco & Jacquemin, 2011b; Gorb et al., 2004; Florian et al., 1995; Florian & Leszczynski, 1996; Villani, 2005, 2006, 2010).

After a comprehensive literature review we came to a conclusion that although it is widely accepted that mutations *in vivo* play a very important role in cell functioning, elementary physico-chemical mechanisms of this process remain poorly understood.

The questions of existence of different tautomeric forms of nucleic acid bases and their possible role as mutagenic factors are under intense scrutiny. The understanding of the tautomeric behavior of the purine and pyrimidine bases of the nucleic acids is of fundamental importance not only for quantitative concepts of chemical bonding and physical chemistry, but also for molecular biology and the presumed role of the rare tautomers in mutagenesis.

The structural requirements for tautomeric shifts in the base pairs that may initiate mutations have been formulated in literature (Basu et al., 2005): (i) the bases open out during replication phase in their unusual tautomeric condition and (ii) the unusual tautomers form stable base pairs with isosteric Watson-Crick geometry with their wrong suite. Another group of researchers (Da̧bkowska et al., 2005) based on the conclusions earlier reported by Florian et al. (Florian et al., 1994) established that tautomerisation reactions have to fulfill not only thermodynamic but also certain kinetic limits to be relevant to spontaneous DNA mutations. First, the lifetime of the canonical base should be shorter than the reproduction period of a given species. Second, the mutagenic tautomer needs to remain stable during the time period from the occurrence of tautomerisation until the replication process is completed. These conditions impose constraints on barriers for the forward and reverse reactions of DNA bases tautomerisation.

Our purpose in this study is to carefully analyse the molecular mechanisms of spontaneously arising point mutations proposed in literature, to offer truly new ideas for molecular and structural approaches to the nature of spontaneous DNA mutations caused by prototropic tautomerism of nucleotide bases and to provide a novel quantum-chemical insight into the classical understanding of this biologically important problem.

## **2. Computational methods**

62 Quantum Chemistry – Molecules for Innovations

Unusual tautomeric forms of modified bases have been found in damaged DNA duplex, indicating that the transition to such altered forms is indeed feasible (Chatake et al., 1999; Robinson et al., 1998). It is therefore likely that analogues of DNA bases have a propensity to adopt the rare, namely mutagenic tautomeric forms (Brovarets' & Hovorun, 2010b, 2011a). The molecular nature of formation of mutagenic tautomers is not quite clear yet. Several alternative mechanisms of the rare tautomers formation have been discussed in the literature: i) intramolecular proton transfer in DNA bases (Basu et al., 2005; Brovarets' & Hovorun, 2010a, 2010d, 2011a; Gorb et al., 2005; Zhao et al., 2006), ii) proton transfer in a single base assisted by bulk aqueous solution, by micro-hydration or by a single interacting water molecule (Fogarasi, 2008; Furmanchuk et al., 2011; Gorb & Leszczynski, 1998a, 1998b; H.-S. Kim et al., 2007; Michalkova et al., 2008); iii) Löwdin's mechanism of tautomerisation involving double proton transfer (DPT) along two intermolecular hydrogen (H) bonds of

On the basis of the Watson-Crick's model Löwdin (Löwdin, 1963, 1965, 1966) suggested that spontaneous mutagenesis causing aging and cancer could be induced by tautomerisation of Ade・Thy and Gua・Cyt Watson-Crick base pairs through DPT along neighbouring intermolecular H-bonds joining bases in pairs. Following the pioneering Löwdin's work the DNA base pairs have been extensively studied using a wide range of theoretical approaches, essentially in the gas phase (Cerón-Carrasco et al., 2011a; Cerón-Carrasco & Jacquemin, 2011b; Gorb et al., 2004; Florian et al., 1995; Florian & Leszczynski, 1996; Villani, 2005, 2006, 2010).

After a comprehensive literature review we came to a conclusion that although it is widely accepted that mutations *in vivo* play a very important role in cell functioning, elementary

The questions of existence of different tautomeric forms of nucleic acid bases and their possible role as mutagenic factors are under intense scrutiny. The understanding of the tautomeric behavior of the purine and pyrimidine bases of the nucleic acids is of fundamental importance not only for quantitative concepts of chemical bonding and physical chemistry, but also for molecular biology and the presumed role of the rare

The structural requirements for tautomeric shifts in the base pairs that may initiate mutations have been formulated in literature (Basu et al., 2005): (i) the bases open out during replication phase in their unusual tautomeric condition and (ii) the unusual tautomers form stable base pairs with isosteric Watson-Crick geometry with their wrong suite. Another group of researchers (Da̧bkowska et al., 2005) based on the conclusions earlier reported by Florian et al. (Florian et al., 1994) established that tautomerisation reactions have to fulfill not only thermodynamic but also certain kinetic limits to be relevant to spontaneous DNA mutations. First, the lifetime of the canonical base should be shorter than the reproduction period of a given species. Second, the mutagenic tautomer needs to remain stable during the time period from the occurrence of tautomerisation until the replication process is completed. These conditions impose constraints on barriers for the

Our purpose in this study is to carefully analyse the molecular mechanisms of spontaneously arising point mutations proposed in literature, to offer truly new ideas for

physico-chemical mechanisms of this process remain poorly understood.

forward and reverse reactions of DNA bases tautomerisation.

complementary DNA base pairs (Löwdin, 1963, 1965, 1966).

tautomers in mutagenesis.

The *ab initio* methods were used to investigate the tautomerisation of the DNA bases and mispairs involving mutagenic tautomers. All quantum-chemical calculations were performed using the Gaussian 03 program package (Frisch et al., 2003).

Geometries and harmonic vibrational frequencies of molecules and complexes were obtained using Becke's three-parameter exchange functional (B3) (Becke, 1993) combined with Lee, Yang, and Parr's (LYP) correlation functional (Lee et al., 1988) implemented in Gaussian 03 that has good performance for calculating barrier heights, thermo-chemical kinetics or intra- and intermolecular H-bonds in the systems recently studied (Brovarets', 2010; Brovarets' & Hovorun, 2010a, 2010b, 2010d, 2010f, 2011a, 2011b; Brovarets' et al., 2010c, 2010e) and 6-311++G(d,p) basis set. The absence of imaginary vibrational frequencies proved that energy-minimized structures perfectly correspond to the local minima of the potential energy landscape.

To consider electronic correlation effects as accurately as possible, we performed single point energy calculations at the MP2/6-311++G(2df,pd) level of theory for the B3LYP/6- 311++G(d,p) geometries.

As for the transition states (TS) of tautomerisation of the isolated bases or their complexes, they were located by means of Synchronous Transit-guided Quasi-Newton (STQN) method (Peng & Schlegel, 1993; Peng et al., 1996) using the Berny algorithm and proved to contain one and only one imaginary frequency corresponding to the reaction coordinate. Afterwards the reaction pathway of proton transfer was followed by performing an intrinsic reaction coordinate calculation in order to make sure that transition state really connects the expected reactants and products (Gonzalez & Schlegel, 1989). We applied the standard transition state theory (Atkins, 1998) to estimate barriers for tautomerisation reactions.

The equilibrium constants of tautomerisation were calculated using the standard equation K=exp(-ΔG/RT), where ΔG is the relative Gibbs free energy of the reactant or product, T is the absolute temperature, and R is the universal gas constant.

The time τ99.9% necessary to reach 99.9% of the equilibrium concentration of the mutagenic tautomer in the system of reversible first-order forward (k*f*) and reverse (k*r*) reactions (canonical ↔ mutagenic tautomer transitions) can be estimated from the equation (Atkins, 1998)

$$
\tau\_{\text{\\$9.9\%}} = \frac{\ln 10^3}{k\_f + k\_r} \tag{1}
$$

and the lifetime τ and the half-lifetime τ1/2 of the complexes are given by 1/k and ln(2)/k, respectively. We applied the standard transition state theory (Atkins, 1998) in which quantum tunneling effects are accounted by the Wigner's tunnelling correction (Wigner, 1932).

Elementary Molecular Mechanisms of the Spontaneous Point

nonplanar guanine amino group.

been calculated (Y. Wang et al., 1993).

1983; Dolinnaya & Gryaznova, 1989).

**3.1 Pyramidalization of the amine fragment of the Ade** 

Šponer & Hobza, 1994).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 65

reported by Choi et al. (Choi et al., 2008). The mismatched Guaanti·Adeanti base pair (Privé et al., 1987) is an example exhibiting the strong out-of-plane H-bond character related to the

The internal nonplanarity of the amino group originates from the partial sp3 hybridization of the amino group nitrogen atom (Govorun et al., 1992; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Gorb & Leszczynski, 1998a, 1998b; Hobza & Šponer, 1999;

At least one conclusion that may be drawn from these investigations is that the amines could be much more flexible than previously expected because of the low values of the inversion and rotation barriers of the amino group. The inversion dynamics of the amino group have been investigated by *ab initio* methods with and without inclusion of correlation energy utilizing medium and extended basis sets (Bludský et al., 1996) and the barriers for inversion or internal rotation of the amino group in a quasi-classical approximation have

We present herein a more comprehensive analysis of the ≥C-NH2 fragment interconversion in DNA bases - its plane inversion and anisotropic internal rotation of the amino group and its influence on the structural relaxation of the molecular ring. Summary of our findings makes it possible to describe a complex mechanism of the amino group motion which includes tunneling (only for rotations) and large amplitude motion above the barrier of planarization. Of particular interest, in this context, is the phenomenon of pyramidalization. The nitrogenous bases with exocyclic amine fragment ≥C-NH2 are known to have nonrigid structures (for details see (Bludský et al., 1996; Florian et al., 1995; Hovorun & Kondratyuk, 1996; Hovorun et al., 1999)). Their interconversion, i.e. conformational (without breaking chemical bonds) transitions within a molecule, is accomplished in three topologically and energetically distinct ways - plane inversion of the ≥C-NH2 fragment and two, clockwise or counterclockwise, rotations of the amino group around exocyclic С-N bond *via* plane symmetrical transition states with substantially pyramidalized amine fragment. It should be mentioned that in the planar transition state (TS1) of the ≥C-NH2 fragment inversion the exocyclic С-N bond is shortened and the N-H bonds are elongated as compared to those in the nonplanar equilibrium configuration, the valence angle H-N-H becomes close to 120°. In the plane-symmetric transition states of the amino group rotations TS2 and TS3 the С-N bond becomes elongated, the N-H bonds become shortened and the valence angle H-N-H distinctly deviates from 120°, at that the amine fragment ≥C-NH2 is highly pyramidalized as compared to the equilibrium configuration. All these results clearly demonstrate that the structural nonrigidity of nitrogenous bases is determined by intramolecular quantumchemical effect - p-π-conjugation of a lone electron pair (LEP) of the nitrogen atom of the amine fragment ≥C-NH2 with the π-electronic system of the ring (Dolinnaya & Gromova,

So, we demonstrated that Ade (N1C6N6H=0.013°; C5C6N6H=-0.014°) is an effectively planar molecule (effective symmetry Cs) (Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996). Its interconversion is accomplished *via* two plane-symmetric transition states with Gibbs free energy of 14.34 and 14.57 kcal/mol and also through the planar transition state with

$$\Gamma = 1 + \frac{1}{24} \left(\frac{h\nu\_{\dot{I}}}{k\_B T}\right)^2 \tag{2}$$

that is adequate for proton transfer reactions (Brovarets' & Hovorun, 2010a, 2010b, 2011a; Cerón-Carrasco & Jacquemin, 2011b) to estimate the values of rate constants k*f* and k*<sup>r</sup>*

$$k\_{f,r} = \Gamma \cdot \frac{k\_B T}{h} e^{-\frac{\Delta \Lambda \mathcal{G}\_{f,r}}{RT}} \tag{3}$$

where k*B* - the Boltzmann's constant, h *–* the Planck's constant, *ΔΔGf,r –* the Gibbs free energy of activation for the proton transfer reaction, ν*i* – the magnitude of the imaginary frequency associated with the vibrational mode at the transition state that connects reactants and products.

The electronic interaction energies have been computed at the MP2/6-311++G(2df,pd) level of theory for the B3LYP/6-311++G(d,p) geometries. In each case the interaction energy was corrected for the basis set superposition error (BSSE) (Boys & Bernardi, 1970; Gutowski et al., 1986) through the counterpoise procedure (Sordo et al., 1988; Sordo, 2001) implemented in the Gaussian 03 package (Frisch et al., 2003).

The topology of the electron density was analysed using program package AIMAll (AIMAll, 2010) with all the default options. The presence of a bond critical point (BCP), namely the socalled (3,-1) point, and a bond path between hydrogen donor and acceptor, as well as the positive value of the Laplacian at this bond critical point, were considered as the necessary conditions for H-bond formation. Wave functions were obtained at the level of theory used for geometry optimization.

#### **3. DNA bases with amino group: Planar or nonplanar?**

The amino group –NH2 in DNA bases, namely, Gua, Cyt and Ade, plays a key role in formation of H-bonds in nucleic acids and in other molecular systems. Thus, the structure of this group is of fundamental importance in the molecular recognition phenomena. The DNA bases were believed to be planar for many years, until the nonplanarity of their amino groups has been predicted in the 1990s (Aamouche et al., 1997; Hobza & Šponer, 1999; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Komarov & Polozov, 1990; Komarov et al., 1992; Šponer & Hobza, 1994; Šponer et al., 2001). Direct experimental results for the nucleic acid bases amino moieties are not available, but indirect experimental evidence does exist. The first indirect experimental evidence was connected with the excellent agreement between the theoretical anharmonic (Bludský et al., 1996) and experimental inversion-torsion (Kydd & Krueger, 1977, 1978; Larsen et al., 1976) vibrational frequencies that provided evidence concerning the nature of the predicted aniline potential energy surface, consistent with a strong nonplanarity of the amino group (Lister et al., 1974; Sinclair & Pratt, 1996; Quack & Stockburger, 1972).

Although a noticeable inertial defect of Ade was observed in a microwave study (Brown et al., 1989a), its source was not directly related to the nonplanarity of this base. Indirect experimental evidence was associated with the vibrational transition moment angles of Ade

<sup>1</sup> <sup>1</sup> 24

Cerón-Carrasco & Jacquemin, 2011b) to estimate the values of rate constants k*f* and k*<sup>r</sup>*

*k T k e h*

,

*f r*

in the Gaussian 03 package (Frisch et al., 2003).

**3. DNA bases with amino group: Planar or nonplanar?** 

Sinclair & Pratt, 1996; Quack & Stockburger, 1972).

for geometry optimization.

products.

that is adequate for proton transfer reactions (Brovarets' & Hovorun, 2010a, 2010b, 2011a;

where k*B* - the Boltzmann's constant, h *–* the Planck's constant, *ΔΔGf,r –* the Gibbs free energy of activation for the proton transfer reaction, ν*i* – the magnitude of the imaginary frequency associated with the vibrational mode at the transition state that connects reactants and

The electronic interaction energies have been computed at the MP2/6-311++G(2df,pd) level of theory for the B3LYP/6-311++G(d,p) geometries. In each case the interaction energy was corrected for the basis set superposition error (BSSE) (Boys & Bernardi, 1970; Gutowski et al., 1986) through the counterpoise procedure (Sordo et al., 1988; Sordo, 2001) implemented

The topology of the electron density was analysed using program package AIMAll (AIMAll, 2010) with all the default options. The presence of a bond critical point (BCP), namely the socalled (3,-1) point, and a bond path between hydrogen donor and acceptor, as well as the positive value of the Laplacian at this bond critical point, were considered as the necessary conditions for H-bond formation. Wave functions were obtained at the level of theory used

The amino group –NH2 in DNA bases, namely, Gua, Cyt and Ade, plays a key role in formation of H-bonds in nucleic acids and in other molecular systems. Thus, the structure of this group is of fundamental importance in the molecular recognition phenomena. The DNA bases were believed to be planar for many years, until the nonplanarity of their amino groups has been predicted in the 1990s (Aamouche et al., 1997; Hobza & Šponer, 1999; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Komarov & Polozov, 1990; Komarov et al., 1992; Šponer & Hobza, 1994; Šponer et al., 2001). Direct experimental results for the nucleic acid bases amino moieties are not available, but indirect experimental evidence does exist. The first indirect experimental evidence was connected with the excellent agreement between the theoretical anharmonic (Bludský et al., 1996) and experimental inversion-torsion (Kydd & Krueger, 1977, 1978; Larsen et al., 1976) vibrational frequencies that provided evidence concerning the nature of the predicted aniline potential energy surface, consistent with a strong nonplanarity of the amino group (Lister et al., 1974;

Although a noticeable inertial defect of Ade was observed in a microwave study (Brown et al., 1989a), its source was not directly related to the nonplanarity of this base. Indirect experimental evidence was associated with the vibrational transition moment angles of Ade

2

,

(3)

*Gf r B RT*

 

(2)

*h i k T B*

 

 

reported by Choi et al. (Choi et al., 2008). The mismatched Guaanti·Adeanti base pair (Privé et al., 1987) is an example exhibiting the strong out-of-plane H-bond character related to the nonplanar guanine amino group.

The internal nonplanarity of the amino group originates from the partial sp3 hybridization of the amino group nitrogen atom (Govorun et al., 1992; Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996; Gorb & Leszczynski, 1998a, 1998b; Hobza & Šponer, 1999; Šponer & Hobza, 1994).

At least one conclusion that may be drawn from these investigations is that the amines could be much more flexible than previously expected because of the low values of the inversion and rotation barriers of the amino group. The inversion dynamics of the amino group have been investigated by *ab initio* methods with and without inclusion of correlation energy utilizing medium and extended basis sets (Bludský et al., 1996) and the barriers for inversion or internal rotation of the amino group in a quasi-classical approximation have been calculated (Y. Wang et al., 1993).

We present herein a more comprehensive analysis of the ≥C-NH2 fragment interconversion in DNA bases - its plane inversion and anisotropic internal rotation of the amino group and its influence on the structural relaxation of the molecular ring. Summary of our findings makes it possible to describe a complex mechanism of the amino group motion which includes tunneling (only for rotations) and large amplitude motion above the barrier of planarization. Of particular interest, in this context, is the phenomenon of pyramidalization.

The nitrogenous bases with exocyclic amine fragment ≥C-NH2 are known to have nonrigid structures (for details see (Bludský et al., 1996; Florian et al., 1995; Hovorun & Kondratyuk, 1996; Hovorun et al., 1999)). Their interconversion, i.e. conformational (without breaking chemical bonds) transitions within a molecule, is accomplished in three topologically and energetically distinct ways - plane inversion of the ≥C-NH2 fragment and two, clockwise or counterclockwise, rotations of the amino group around exocyclic С-N bond *via* plane symmetrical transition states with substantially pyramidalized amine fragment. It should be mentioned that in the planar transition state (TS1) of the ≥C-NH2 fragment inversion the exocyclic С-N bond is shortened and the N-H bonds are elongated as compared to those in the nonplanar equilibrium configuration, the valence angle H-N-H becomes close to 120°. In the plane-symmetric transition states of the amino group rotations TS2 and TS3 the С-N bond becomes elongated, the N-H bonds become shortened and the valence angle H-N-H distinctly deviates from 120°, at that the amine fragment ≥C-NH2 is highly pyramidalized as compared to the equilibrium configuration. All these results clearly demonstrate that the structural nonrigidity of nitrogenous bases is determined by intramolecular quantumchemical effect - p-π-conjugation of a lone electron pair (LEP) of the nitrogen atom of the amine fragment ≥C-NH2 with the π-electronic system of the ring (Dolinnaya & Gromova, 1983; Dolinnaya & Gryaznova, 1989).

#### **3.1 Pyramidalization of the amine fragment of the Ade**

So, we demonstrated that Ade (N1C6N6H=0.013°; C5C6N6H=-0.014°) is an effectively planar molecule (effective symmetry Cs) (Hovorun et al., 1995a, 1995b, 1999; Hovorun & Kondratyuk, 1996). Its interconversion is accomplished *via* two plane-symmetric transition states with Gibbs free energy of 14.34 and 14.57 kcal/mol and also through the planar transition state with

Elementary Molecular Mechanisms of the Spontaneous Point

Hovorun, 2010b).

2011a).

hydrogen atom of the C5-H group).

planarization electronic energy barrier (0.91 kcal/mol or 318.6 cm-1).

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

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 67

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

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

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).

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,

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

the activation energy of 0.12 kcal/mol1 (Table 1). MP2 complete basis set limit method with the aug-cc-pVTZ → aug-cc-pVQZ (aTZ → aQZ) extrapolation scheme has predicted very small planarization barrier of the Ade amino group, 0.015 kcal/mol (Zierkiewicz et al., 2008), which is in very good agreement with the MP2-predicted planarization barrier of 0.020 kcal/mol reported by Wang and Schaefer III (S. Wang & Schaefer III, 2006). Similar results were calculated using coupled cluster CCSD(T) complete basis set method – 0.125 kcal/mol (Zierkiewicz et al., 2008). Thus, the literature review highlights that the amino group in isolated Ade, in the gas phase, is very flexible with a small degree of nonplanarity.


\* - values obtained at the MP2/6-311++G(2df,pd)//B3LYP/cc-pVDZ level of theory (Brovarets' & Hovorun, 2010b);
