PCCP PAPER. Introduction. Ol ha O. Brovarets abc and Dmytro M. Hovorun* abc. View Article Online View Journal

Transcription

1 PAPER View Article Online View Journal Cite this: DOI: /c3cp52644e Received 25th June 2013, Accepted 20th September 2013 DOI: /c3cp52644e Atomistic nature of the DPT tautomerisation of the biologically important CC* DNA base mispair containing amino and imino tautomers of cytosine: a QM and QTAIM approach Ol ha O. Brovarets abc and Dmytro M. Hovorun* abc A theoretical study of tautomerisation of the biologically important cytosinecytosine* (CC*) DNA mismatch with a propeller-like structure ( C4N3N3C4 = 32.41; C 1 symmetry) and cis-oriented N1H glycosidic bonds, formed by the amino and imino tautomers of the C nucleobase, via the asynchronous concerted double proton transfer (DPT) along two H-bonds through the transition state (TS CC*2C*C ) ( C4N3N3C4 = 48.51; C 1 symmetry) into the C*C mispair was carried out for the first time. It was established that the CC*/C*C DNA base mispair is associated by the antiparallel N4HN4 (6.66 kcal mol 1 ), N3HN3 (6.47 kcal mol 1 ) H-bonds and the O2O2 van der Waals (vdw) contact (0.33 kcal mol 1 ), while the zwitterionic TS CC*2C*C is stabilized by the parallel N4 + HN4 (13.55 kcal mol 1 ), N3 + HN3 (13.20 kcal mol 1 ) H-bonds and the O2 + O2 vdw contact (0.60 kcal mol 1 ). It was shown that the CC* 2 C*C tautomerisation via the DPT is assisted by the O2O2 vdw contact, that in contrast to the two others N4HN4 and N3HN3 H-bonds exists along the entire intrinsic reaction coordinate (IRC) range. The positive values of the Grunenberg s compliance constants ( and Å mdyn 1 for CC*/C*C andts CC*2C*C, respectively) indicate that the O2O2 vdw contact is a stabilizing closed-shell interaction. It was found that the middle N3HN3 H-bond is anti-cooperative with the upper N4HN4 H-bond and cooperative with the lower O2O2 vdw contact. The 9 key points, which can be considered as electron-topological fingerprints of the asynchronous concerted CC* 2 C*C tautomerisation process via the DPT were revealed along the IRC and examined in detail. It was shown that the CC*/C*C base mispair is a thermodynamically and dynamically stable structure. Its lifetime is equal to sat the MP2/cc-pVQZ//B3LYP/ G(d,p) level of theory in vacuum. All 6 low-frequency intermolecular vibrations are able to develop during this time span. Introduction The nature of the incorrect pyrimidine pyrimidine base mispairs (TT, CT and CC), which can cause transversions, is one of the least studied aspects of the theory of spontaneous point mutations. 1 The CC base mispair is incorporated into the DNA during its synthesis with the lowest frequency among these three base mispairs. 2 However, it is not practically eliminated from the E.coli genome in the process of its repair. 3,4 a Department of Molecular and Quantum Biophysics, Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, 150 Akademika Zabolotnoho Str., Kyiv, Ukraine. dhovorun@imbg.org.ua b Research and Educational Center State Key Laboratory of Molecular and Cell Biology, 150 Akademika Zabolotnoho Str., Kyiv, Ukraine c Department of Molecular Biotechnology and Bioinformatics, Institute of High Technologies, Taras Shevchenko National University of Kyiv, 2-h Akademika Hlushkova Ave., Kyiv, Ukraine Currently, the CC base mispair has been the subject of several comprehensive studies using the physico-chemical methods Thus, its remarkable features to be electroneutral and stabilized solely by only one intermolecular H-bond and stacking interactions with the neighboring complementary base pairs, which were revealed in the double-stranded DNA at neutral ph, seems to be well documented through many experiments, ranging from NMR spectroscopy to molecular dynamics simulations. 5,6 The CC base mispair in the wobble configuration as well as others pyrimidine pyrimidine base pairs do not cause significant local structural perturbations of the DNA sugar phosphate backbone, however, in contrast to others base pairs, thermodynamic destabilization of the CC duplex involves 7 9 base pairs. 7 It was found in a work by Schlick et al., 11 using molecular dynamics, that the wobble configuration of the CC base mispair is not competent in terms of its enzymatic incorporation into the DNA structure, This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys.

2 since it does not allow DNA polymerase to switch from its open to the closed active conformation. Recently, we have suggested that the CC* base pair involving C* imino tautomer (here and below the mutagenic imino tautomer of the C base is marked with an asterisk) is the biologically competent configuration of the CC base mispair, causing spontaneous transversions. 20,21 We have also shown that the geometrical sizes of the CC* base pair in the transition state of its planarization are closer to the similar Watson Crick sizes comparably with the CC* base pair. 20 Interestingly, the CC* base mispair with cis-oriented N1H glycosidic bonds was also fixed in the rrna by X-ray analysis. 22 In this work, the authors consider it as a static structure in which hydrogen atoms are involved in the intermolecular H-bonds, localized in one of the two possible minima of the potential energy. This paper is focused on the study of dynamical behavior of the CC* base mispair, namely on the elucidation of physicochemical mechanisms of its tautomerisation through the double proton transfer (DPT). This issue has not been previously raised in the literature before. Such formulation of the task is important from the perspective of the theory of spontaneous point mutations, as well as from the point of view of molecular bioelectronics, offering an attractive possibility to detect and identify irregular base pairs within the structure of the DNA double helix So, we were the first to investigate in detail Löwdin s mechanism of the CC* 2 C*C mutagenic tautomerisation via the DPT. In this paper we report a physico-chemical study of the structural, electron-topological, energetical and polar properties of the biologically important CC* base mispair and the atomistic nature of the CC* 2 C*C mutagenic tautomerisation through the DPT. The sweeps of the energetic, electron-topological, geometric and polar parameters, which describe the course of the CC* 2 C*C tautomerisation along the intrinsic reaction coordinate (IRC) have been established for the first time. It was found using these data, that the CC* 2 C*C tautomerisation via DPT is concerted (i.e., this reaction involves no stable intermediates) and asynchronous (i.e., both protons involved in the N4HN4 and N3HN3 H-bonds move with a time gap) process. It was shown that the propeller-like CC*/C*C base pair ( C4N3N3C4 = 32.41; C 1 symmetry) is thermodynamically (DG int = 2.34 kcal mol 1 ) and dynamically (zero-point energy E ZPE = cm 1 of the corresponding vibrational mode, the frequency of which becomes imaginary at the transition state (TS CC*2C*C ), is less than the value of the reverse barrier DDE TS = cm 1 obtained at the MP2/cc-pVQZ//B3LYP/ G(d,p) level of quantum-mechanical (QM) theory) stable structure, and even much more stable than the base pairs that were previously investigated by us Its lifetime is equal to s at the MP2/ cc-pvqz//b3lyp/ g(d,p) level of theory in vacuum. All 6low-frequency 32 intermolecular vibrations (27.4, 34.9, 49.3, 77.5, 95.8 and cm 1 ) are able to develop during this period of time. Computational methods All calculations have been carried out with the Gaussian 09 suite of programs. 33 Geometries and harmonic vibrational frequencies of the CC* and C*C DNA base mispairs and the TS CC*2C*C of their mutagenic tautomerisation via the DPT were obtained using density functional theory (DFT) 34 with the B3LYP hybrid functional, 35 which includes Becke s threeparameter exchange functional (B3) 36 combined with Lee, Yang and Parr s (LYP) correlation functional 37 in connection with G(d,p) Pople-type basis set in vacuum. A scaling factor of was used in the present work at the B3LYP QM level of theory to correct the harmonic frequencies of all studied structures. We performed single point energy calculations at the correlated MP2 level of theory 43 with the G(2df,pd) Pople-type and cc-pvtz/cc-pvqz Dunning-type 47,48 basis sets for the B3LYP/ G(d,p) geometries to consider electronic correlation effects as accurately as possible. MP2/ G(2df,pd)// B3LYP/ G(d,p), MP2/cc-pVTZ//B3LYP/ G(d,p) and MP2/cc-pVQZ//B3LYP/ G(d,p) levels of QM theory have been successfully applied on similar systems studied recently, and have been verified to give accurate normal mode frequencies, barrier heights, characteristics of intra- and intermolecular H-bonds and geometries ,40 Moreover, an excellent agreement between computational and experimental NMR, UV and IR spectroscopic data 49,50 evidences that the levels of theory applied for the single-point energy calculations (MP2/ G(2df,pd), MP2/cc-pVTZ and MP2/cc-pVQZ), as well as the method employed for the geometry optimisation (B3LYP/ G(d,p)) are reliable. The DFT method has been recommended in the literature for describing the tautomerisation phenomena of H-bonded nucleobase pairs since it has shown a good balance between computational cost and accuracy, and therefore can be considered as the shortest way to MP2 results. 28,51,52 Furthermore, the DFT method has also proved to be hugely popular with the study of the vibrations of the constituents of nucleic acids. 32,41 The correspondence of the stationary points to the local minimum or TS CC*2C*C on the potential energy landscape has been checked by the absence or the presence, respectively, of one and only one imaginary frequency, corresponding to the normal mode that identifies the reaction coordinate. TS CC*2C*C was located by means of the synchronous transit-guided quasi- Newton (STQN) method. 53,54 Since the stationary points and TS CC*2C*C were located, the reaction pathway was established by following the IRC in the forward and reverse directions from the TS using the Hessianbased predictor-corrector (HPC) integration algorithm with tight convergence criteria. These calculations eventually ensure that the proper reaction pathway, connecting the expected reactants and products on each side of the TS, has been found. We have investigated the evolution of the energetic, geometric, polar and electron-topological characteristics of the H-bonds and base pairs along the reaction pathway, establishing them at each point of the IRC. The electronic interaction energies E int have been computed at the MP2/ G(2df,pd) level of theory for the geometries optimised at the DFT B3LYP/ G(d,p) level of theory as the difference between the total energy of the base pair and the energies of the isolated monomers. In each case, the interaction Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013

3 energy was corrected for the basis set superposition error (BSSE) 58,59 through the counterpoise procedure. 60,61 The Gibbs free energy G values for all structures were obtained at room temperature (T = K) in the following way: G = E el + E corr, (1) where E el is the electronic energy, E corr the thermal correction. The lifetime t of the CC* and C*C DNA mispairs was calculated using the formula 1/k f,r. The time t 99.9% necessary to reach 99.9% of the equilibrium concentration of the CC* reactant and the C*C product of the reaction in the system of reversible first-order forward (k f ) and reverse (k r ) reactions was estimated using the formula: 62 t 99:9% ¼ ln103 : (2) k f þ k r To estimate the values of the forward k f and reverse k r rate constants for the CC* 2 C*C tautomerisation reaction: k f;r ¼ G k DDG BT f;r h e RT (3) we applied the standard TS theory, 62 in which quantum tunneling effects are accounted by the Wigner s tunneling correction, 63 that is adequate for the DPT reactions: 28 31,40 G ¼ 1 þ 1 hn 2 i ; (4) 24 k B T where k B is the Boltzmann constant, T absolute temperature, h Planck s constant, DDG f,r the Gibbs free energy of activation for the forward and reverse DPT reactions (T = K), R universal gas constant, n i the magnitude of the imaginary frequency associated with the vibrational mode at the TS that connects reactants and products. Bader s quantum theory Atoms in molecules (QTAIM) was applied to analyse electron density distribution. 64 The topology of the electron density distribution has been examined in detail using the program package AIMAll 65 with all the default options. Wave functions were obtained at the level of theory used for geometry optimisation. The presence of a bond critical point (BCP), 64 namely the so-called (3, 1) BCP and a bond path between hydrogen donor and acceptor, as well as the positive value of the Laplacian at this BCP (Dr Z 0), were considered as the criteria for the formation of van der Waals (vdw) contact and H-bond The energies of the conventional intermolecular H-bonds E HB in the CC* and C*C base pairs were evaluated by the empirical Iogansen s formula: 71 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E HB ¼ 0:33 Dn 40; (5) where Dn is the the magnitude of the redshift (relative to the free molecule) of the stretching mode of H-bonded groups involved in the H-bonding. The partial deuteration, namely the semi-deuteration of the NH imino and NH 2 amino groups, was applied to eliminate the effect of vibrational resonances. 28,40,70 The energies of the O2O2 vdw contact E O2O2 and of all intermolecular H-bonds E HB under the investigation of the sweeps of their energies were evaluated by the empirical Espinosa Molins Lecomte (EML) formula, 72,73 based on the electron density distribution at the (3, 1) BCPs of the H-bonds and of the O2O2 vdw contact: E HB/O2O2 = 0.5V(r), (6) where V(r) is the the value of a local potential energy density at the (3, 1) BCPs. Moreover, the relative strength of the O2O2 vdw contact was estimated by means of Grunenberg s compliance constants formalism In contrast to the force constants, the numerical values of compliance constants do not depend on the coordinate system. The physical meaning of compliance constants is deduced from their definition as a partial second derivative of the potential energy due to an external force: C ij j : (7) In other words, compliance constants measure the displacement of an internal coordinate resulting from a unit force acting on it. As follows from this definition, a lower numerical value of a compliance constant represents a stronger bond. The compliance constants were calculated using the Compliance program. 74,75 A period of the intermolecular vibrations T is calculated as: T ¼ 1 nc ; (8) where n is the frequency of vibrations, c the speed of light in vacuum. The frequency f of the CC* 2 C*C tautomerisation was estimated using the formula: f ¼ 1 (9) t where t is the lifetime of the CC*/C*C base pair. The atomic numbering scheme for the nucleobase is conventional. 77 Results and discussion Structural and energetic features of the CC*/C*C DNA base mispairs, TS CC*2C*C and intermolecular specific interactions stabilizing them The obtained results are presented numerically in Tables 1 3 and graphically in Scheme 1 and Fig We start their discussion from the structural and energetical characteristics of the CC* and C*C DNA base mispairs and TS CC*2C*C of their tautomerisation via the DPT, for which we consider only one out of the two mirror-symmetric conformers (enantiomers), since they are equivalent from a structural and energetical point of view and do not require separate analysis. The biologically important CC* base mispair, distinguished in the literature as short Watson Crick base pair, 22 is essentially a nonplanar and propeller-like structure (+C4N3(C)N3C4(C*) = 32.41) with C 1 symmetry (Fig. 1 and 9). The heterocycles of the C and C* bases as well as others DNA bases remain almost planar in This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys.

4 Table 1 Electron-topological, structural, vibrational and energetical characteristics of the intermolecular H-bonds and the O2O2 vdw contact revealed in the CC*, C*C and TS CC*2C*C obtained at the B3LYP/ G(d,p) level of theory in vacuum Complex AHB H-bond/vdW contact r a Dr b 100e c d d AB /d O2O2 d HB e Dd AH f +AHB g Dn h E HB /E O2O2 i CC*/C*C (IRC = 7.47/6.89 Bohr) N4HN N3HN O2O * TS CC*2C*C (IRC = 0.00 Bohr) N4 + HN N3 + HN O2 + O * a The electron density at the BCP, a.u. b The Laplacian of the electron density at the BCP, a.u. c The ellipticity at the BCP. d Distance between A (H-bond donor) and B (H-bond acceptor) atoms of the AHB H-bond and between O2 oxygen atoms of the vdw contact, Å. e The distance between H and B atoms, Å. f The elongation of the H-bond donating group AH upon the AHB H-bonding, Å. g The H-bond angle, degree. h The redshift of the stretching vibrational mode of the AH H-bonded group, cm 1. i Energy of the H-bonds, estimated by Iogansen s formula, 71 and energy of the O2O2 vdw contact, estimated by the Espinose Molins Lecomte formula (marked with an asterisk), 72,73 kcal mol 1. Table 2 Electron-topological and structural characteristics of the intermolecular H-bonds and the O2O2 vdw contact revealed in the 9 key points, obtained at the B3LYP/ G(d,p) level of theory in vacuum, and polarity of the latters a Complex AHB H-bond/ vdw contact r Dr 100e d AB /d O2O2 d HB +AHB m b Key point 1/9 (CC*/C*C): IRC = 7.47/6.89 Bohr N4HN N3HN O2O Key point 2 (Dr HN4 = 0): IRC = 0.56 Bohr N4HN N3HN O2O Key point 3 (r N4 H = r H N4 ): IRC = 0.35 Bohr N4 H N N3HN O2O Key point 4 (Dr N4H = 0): IRC = 0.09 Bohr N4HN N3HN O2O Key point 5 (TS CC*2C*C ): IRC = 0.00 Bohr N4 + HN N3 + HN O2 + O Key point 6 (Dr N3H = 0): IRC = 0.15 Bohr N4HN N3HN O2O Key point 7 (r N3 H = r H N3 ): IRC = 0.42 Bohr N4HN N3 H N O2O Key point 8 (Dr HN3 = 0): IRC = 0.62 Bohr N4HN N3HN O2O Notes: a For footnote definitions see Table 1. b m the dipole moment of the complex, D. Table 3 Energetic and kinetic characteristics of the CC* 2 C*C tautomerisation via the DPT in vacuo obtained at different levels of QM theory Level of QM theory DDG TS a DDE TS b kcal mol 1 MP2/ G(2df,pd)//B3LYP/ G(d,p) MP2/cc-pVTZ//B3LYP/ G(d,p) MP2/cc-pVQZ//B3LYP/ G(d,p) a The Gibbs free energy of activation for the CC* 2 C*C tautomerisation via the DPT (T = K), kcal mol 1. b The activation electronic energy for the CC* 2 C*C tautomerisation via the DPT, kcal mol 1 or cm 1. c The frequency of the vibrational mode in the CC*/C*Cbasepair,whichbecomes imaginary in the TS CC*2C*C of the CC* 2 C*C tautomerisation obtained at the B3LYP/ G(d,p) level of geometry optimisation, cm 1. d The zero-point vibrational energy associated with this normal mode, cm 1. e The lifetime of the CC*/C*C base pair, s. f The time necessary to reach 99.9% of the equilibrium concentration of the CC* reactant and the C*C product of the CC* 2 C*C tautomerisation via the DPT, s. cm 1 n c E ZPE d t e t 99.9% f Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013

5 View Article Online Scheme 1 Change in magnitude and orientation of the dipole moment vector at the C* C - C C* (upper row) and C C* - C* C (lower row) tautomerisations through the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. The structures corresponding to the stationary points and their dipole moments are presented. Fig. 1 Geometric structures of the 9 key points describing the evolution of the C C* 2 C* C tautomerisation via the DPT along the IRC obtained at the B3LYP/ G(d,p) level of theory in vacuo. Coordinates of the 9 key points are presented for each structure. The dotted lines indicate the AH B H-bonds and the O2 O2 vdw contact, while continuous lines show covalent bonds (their lengths are presented in angstroms). Carbon atoms are in light-blue, nitrogen in dark-blue, hydrogen in grey and oxygen in red. the base pair, despite the fact that they are flexible molecules.42,78,79 The C C*/C* C mismatches with cis-oriented N1H glycosidic bonds are stabilized by the two antiparallel N4H N4 (6.66 kcal mol 1) and N3H N3 (6.47 kcal mol 1) H-bonds, which are almost energetically equivalent, and the O2 O2 vdw contact This journal is c the Owner Societies 2013 (0.33 kcal mol 1) (Table 1 and Fig. 1). It is evident that the O2 O2 vdw contact, exposed in the minor groove of the double-stranded DNA, is the weakest interaction. The non-planar TSC C*2C* C with a propeller- and ion-pair like structure (DDGTS = 8.28 kcal mol 1 and DDETS = kcal mol 1) Phys. Chem. Chem. Phys.

6 Fig. 2 Profiles of: (a) the electronic energy E and (b) the first derivative of the electronic energy with respect to the IRC de/dirc along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. Profile DE(IRC) is Lorentzian y ¼ 0:09 þ 67:83 p 1:82 4ðx 0:03Þ 2 þ 3:33. Fig. 3 Profile of the dipole moment m along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. with imaginary frequency n i = 520.8i cm 1 and C 1 symmetry (+C4N3(C)N3C4(C*) = 48.51), is stabilized by the two parallel N4 + HN4 (13.55 kcal mol 1 )andn3 + HN3 (13.20 kcal mol 1 ) H-bonds and the O2 + O2 vdw contact (0.60 kcal mol 1 ) (Table 1 and Fig. 1). The values of the electron density r at the (3, 1) BCPs of the H-bonds and the vdw contacts, usually treated as a measure of these interactions, range from a.u. for the O2O2 vdw contact in the CC*/C*C mispair to the a.u. for the N4 + HN4 H-bond in the TS CC*2C*C, that is consistent with the energetical data (Tables 1 and 2). The Laplacian of the electron density Dr at the (3, 1) BCPs is positive for all intrapair interactions and ranges from a.u. for the O2O2 vdw contact to the a.u. for the N4HN4 H-bond in the CC*/ C*C mispair (Tables 1 and 2), demonstrating that H-bonds and vdw contact are attractive closed-shell interactions The value of the Grunenberg s compliance constant for the O2O2 vdw contact equals and Å mdyn 1 in the CC*/C*C and TS CC*2C*C, respectively, indicating that it is a stabilizing closed-shell interaction. 76 These values of the Grunenberg s compliance constants show that the O2O2 vdw contact is an attractive interaction. Thus, the higher value of Grunenberg s compliance constant corresponds to the lower energy of the O2O2 vdw contact, that is consistent with the theoretical concepts The classical geometrical criteria used for identifying the H-bonds are satisfied for all H-bonds in the CC*/C*C base pair and TS CC* 2 C*C : the d HN4/N3 distances (1.458 to Å) are less than the sum of the corresponding Bondi s 80 van der Waals radii (2.75 Å). The positive value of an elongation of the proton donor group AH upon the formation of the conventional H-bond and the angle of H-bonding, which is B1741 (for more details, see Tables 1 and 2), are also the trends of H-bonds. The spectroscopic data collected in Table 1 confirm geometrical results. The shift in the frequency of the stretching mode of the AH donor group (the difference between the frequency for the AH group in monomer and in the base pair) is positive (shift to the red) for all H-bonds. Thermodynamic and dynamic (vibrational) stability of the CC*/C*C DNA base mispairs The CC*/C*C DNA base mispairs examined in the present study are thermodynamically stable structures, since their Gibbs free energy of interaction (DG int = 2.34 kcal mol 1 )islessthan zero and they are even nearly doubly stable than the AT Watson Crick DNA base pair (DG int = 1.43 kcal mol 1 ) at room temperature. It is important to recall that the H-bonds and vdw contact make a dominant contribution into the stabilization (DE int = kcal mol 1 ) of the CC*/C*C base mispairs ((E N4HN4 + E N3HN3 + E O2O2 )/ DE int = 91.2%). This energy relationship can not be considered as the unique physico-chemical characteristics of the exceptionally CC* and C*C basepairs, that are one and the same from a symmetric point of view, and was also observed for the others H-bonded base pairs ,38,40,70,81 It was established by comparing the electronic energy of the reverse barrier of the CC* - C*C tautomerisation DDE = cm 1 obtained at the MP2/cc-pVQZ//B3LYP/ G(d,p) level of QM theory with the zero-point energy E ZPE =1519.2cm 1 of the corresponding vibrational mode, the frequency of which becomes imaginary in the TS CC* 2 C*C, that the CC*/C*C mispair is a dynamically (vibrationally) stable structure Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013

7 Fig. 4 Profiles of: (a) the electron density r; (b) the Laplacian of the electron density Dr, (c) the ellipticity e and (d) the energy of the H-bond E HB, estimated by the EML formula, 72,73 at the BCPs of the covalent and hydrogen bonds along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. (Table 3 and Fig. 1) and even much more stable than the previously investigated by us base pairs ,81 83 Moreover, this statement is objective and does not depend on the chosen quantum-chemical level of theory (Table 3). It was established that all 6 low-frequency 32 intermolecular vibrations (27.4, 34.9, 49.3, 77.5, 95.8 and cm 1 )candevelop during the lifetime t of the CC*/C*C mispairs (t = s obtained at the MP2/cc-pVQZ//B3LYP/ G(d,p) level of QM theory), since their periods T ( , , , , , s, respectively) are noticeably less than this time interval. This observation additionally indicates that the CC*/C*C base pair is a dynamically stable structure ,81 83 The time t 99.9% necessary to reach 99.9% of the equilibrium concentration of the starting CC* and the final C*C base pairs is equal to s at the MP2/cc-pVQZ//B3LYP/ G(d,p) level of QM theory (Table 3). The CC* 2 C*C Löwdin s tautomerisation via the DPT is the periodic dipole-active process (Tables 1 and 2, Scheme 1, Fig. 3) that occurs with frequency 6.53 MHz. Structural and electron-topological architecture of the established 9 key points along the IRC of the CC* 2 C*C tautomerisation through the DPT In order to investigate the energetic, structural, polar and electron-topological reorganizations of the CC* base pair and intermolecular interactions stabilizing it along the IRC, we have performed calculations of the electronic energy, the first derivative of the electronic energy with respect to the IRC, the dipole moment of the base pair, the distances and angle of the intermolecular H-bonds, the electron density, Laplacian of the electron density, ellipticity and the energy at the (3, 1) BCPs of the intrapair H-bonds and vdw contact, the NBO charges of the hydrogen atoms involved in the tautomerisation, the glycosidic angles and the distance between the glycosidic hydrogens at each step along the IRC of the CC* 2 C*C tautomerisation. In such a way we obtained the scanning (so-called sweeps) of these characteristics presented in Fig We revealed 9 key points for the CC* 2 C*C tautomerisation, based on the alterations of the electron density and geometry of the intermolecular H-bonds in the CC* base pair along the IRC of the CC* 2 C*C tautomerisation (Fig. 2, 4a, b and 5b) Key point 1, IRC = 7.47 Bohr. The starting structure along the IRC pathway is the CC* DNA base mispair with Watson Crick geometry, stabilized by the N4HN4 and N3HN3 H-bonds and the O2O2 vdw contact (Tables 1 and 2, Fig. 2 and 4d). Key point 2, IRC = 0.56 Bohr. The structure of the base pair, for which the N4 H chemical bond of the C base is significantly weakened and the HN4 H-bond actually becomes the H N4 This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys.

8 Fig. 5 Profiles of: (a) the distance d AB between the electronegative A and B atoms, (b) the distance d AH/HB between the hydrogen and electronegative A or B atoms and (c) the angle +AHB of the AHB H-bonds along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. covalent bond (Dr HN4 = 0) (Fig. 2 and 4b). The maximum value of the energy of the HN4 H-bond is reached at this key point (Fig. 4d). Interestingly, that one out of the two extrema of the first derivative of the electron energy with respect to the IRC de/dirc (well known in the literature as reaction force )is reached exactly at this key point (Fig. 2). Moreover, precisely at key point 2 the C and C* bases, acting in this case as the reagents of the DPT reaction, lose their chemical individuality, since the HN4 H-bond begins to transform into the H N4 covalent bond. Key point 3, IRC = 0.35 Bohr. This structure is characterized by the equivalent loosened N4 H and H N4 covalent bonds. Dependencies of the geometrical and electron-topological characteristics at the BCPs of these equivalent chemical bonds intersect exactly at this key point, forming w-like graphs for the loosened N4 H N4 covalent bridge (r N4 H = r H N4 = a.u.; Dr N4 H = Dr H N4 = a.u.; d N4 H = d H N4 =1.297Å;d N4N4 = Å; +N4 H N4 = ) (Tables 1 and 2, Fig. 2, 4a, b and 5). Key point 4, IRC = 0.09 Bohr. At this structure situated quite close to the TS CC*2C*C the N4 H covalent bond becomes the N4H H-bond (Fig. 2). A characteristic feature of this structure is a zero value of the Dr at the (3, 1) BCP of the N4H H-bond (Fig. 4b). The maximum value of the energy of the N4H H-bond is attained at this key point (Fig. 4d). Key point 5, IRC = 0.00 Bohr. The TS CC*2C*C of the tautomerisation via the DPT, which itself represents an ion pair C + C, is stabilized by the N4 + HN4 and N3 + HN3 canonical H-bonds and the O2 + O2 vdw contact (Tables 1 and 2, Fig. 2 and 4d). Key point 6, IRC = 0.15 Bohr. The structure of the base pair, for which the H N3 chemical bond of the C + base is significantly weakened and the N3H H-bond actually becomes the N3 H covalent bond (Dr N3H =0)(Fig.2and4b).Themaximum value of the energy of the N3H H-bond is reached exactly at this key point (Fig. 4d). Key point 7, IRC = 0.42 Bohr. This structure possesses the equivalent loosened N3 H and H N3 covalent bonds. Dependencies of the geometrical and electron-topological characteristics at the BCPs of these equivalent chemical bonds intersect exactly at this key point, forming w-like graphs for the loosened N3 H N3 covalent bridge (r N3 H = r H N3 = a.u.; Dr N3 H = Dr H N3 = a.u.; d N3 H = d H N3 = Å; d N3N3 = Å; +N3 H N3 = ) (Tables 1 and 2, Fig. 2, 4a, b and 5). Key point 8, IRC = 0.62 Bohr. At this structure, which is situated quite close to the final C*C mispair containing amino and imino tautomers of the C base, the H N3 covalent bond becomes the HN3 H-bond (Fig. 2). A characteristic feature of this structure is a zero value of the Dr at the (3, 1) BCP of the HN3 H-bond (Fig. 4b). The maximum value of the energy of the HN3 H-bond is attained at this key point (Fig. 4d). Interestingly, the second extremum of the first derivative of the electron energy with respect to the IRC de/dirc Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013

9 Fig. 6 Profiles of: (a) the electron density r, (b) the Laplacian of the electron density Dr, (c) the ellipticity e, (d) the energy of the O2O2 vdw contact E O2O2, estimated by the EML formula, 72,73 at the (3, 1) BCP and (e) the distance d O2O2 between the O2 oxygen atoms of the O2O2 vdw contact along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. (well known in the literature as reaction force ) is reached exactly at this key point (Fig. 2). It should be noted that precisely at key point 8 the C and C* bases, acting in this case as the products of the DPT reaction, reduce their chemical individuality, since the H N3 covalent bond begins to transform into the HN3 H-bond. Key point 9, IRC = 6.89 Bohr. The final structure is the C*C base mispair, stabilized by the N4HN4 and N3HN3 H-bonds and the O2O2 vdw contact (Tables 1 and 2, Fig. 2 and 4d). These 9 key points were used in this study to divide the reaction pathway into the reactant, TS and product regions of the CC* 2 C*C tautomerisation via the DPT (Fig. 2). This underlying separation can be done quite naturally and unambiguously by taking the reaction force minimum and the reaction force maximum as the boundaries for these regions It was established, based on the analysis of the sweeps of the physico-chemical characteristics of the intermolecular interactions along the IRC, that the reactant and product regions where nucleotide bases do not lose their chemical individuality, are located between key points 1 2 ( 7.47 to 0.56 Bohr) and 8 9 (0.62 to 6.89 Bohr), respectively, where the Laplacian of the electron density Dr at the (3, 1) BCPs of the H-bonds vanishes. The TS region, where eventually the DPT reaction occurs and This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys.

10 Fig. 7 Profiles of the NBO charges of the hydrogen atoms involved in the N4HN4 (H I ) and N3HN3 (H II ) H-bonds along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. where the C and C* bases lose their chemical individuality, since the HN4 and HN3 H-bonds begin to transform into the H N4 and H N3 covalent bonds, respectively, is quite narrow and located between key points 2 and 8 ( 0.56 to 0.62 Bohr). Interestingly, as noted earlier, the extrema of the first derivative of the electron energy with respect to the IRC de/dirc (well known in the literature as reaction force )is reached exactly at key points 2 and 8 (Fig. 2b). This behavior is not an individual physico-chemical property of the investigated base pair. Thorough analysis of the obtained by us earlier results regarding the physico-chemical nature of the DPT in the H-bonded pairs of nucleotide bases 28 31,82,83 allows to state that the aforementioned feature has a general nature and does not depend on the structure of the H-bonded complexes. Thus, the phenomenological approach of the reaction force 90,91 received atomistic, microstructural interpretation. We established that the electronic energy necessary to bring the donor and acceptor atoms as close as possible to each other and to acquire such mutual deformation and orientation, that eventually lead to the DPT reaction, which is the energy difference between key points 2 and 1, is equal to 8.15 kcal mol 1 representing 70.8% of the TS energy. The same amount of electronic energy (8.20 kcal mol 1 ) is released during the relaxation of key point 8 to the C*C product. Evolution of the main physico-chemical properties along the IRC of the CC* 2 C*C tautomerisation through the DPT The strong dependence of both the absolute value and the orientation of the dipole moment m of the studied base pairs on the IRC is presented in Scheme 1 and Fig. 3. The O-like profile of the dipole moment has a sharp pronounced peak exactly at the TS CC*2C*C. The dipole moment significantly changes in the range 4.33 to 5.72 D (Fig. 3). The electron-topological (the electron density r, the Laplacian of the electron density Dr, the ellipticity e and the H-bond energy E HB, calculated by the EML formula, 72,73 at the (3, 1) BCPs) and geometric (the distance d AB between the electronegative A and B atoms, the distance d AH/HB between the hydrogen and electronegative A or B atoms and the angle +AHBoftheAHB H-bond) properties of the intermolecular interations are presented in Fig It is important to note that the upper N4HN4 and the middle N3HN3 H-bonds in the CC* base pair exist within the range from key point 1 to 2 and from key point 1 to 6, respectively, becoming stronger during the tautomerisation process and reaching their maxima at key points 2 and 6, respectively, while the upper N4HN4 and the middle N3HN3 H-bonds in the C*C base pair exist within the range from key point 8 to 9 and from key point 4 to 9, respectively, reaching their maxima at key points 8 and 4, respectively, and becoming weaker during the tautomerisation process in vacuum (Fig. 4d). It should be noted thatonthegraphsisshownonlytheenergyoftheh-bonds corresponding to the value Dr Z 0(Fig.4b). Analysis of the dependencies of the H-bond energies on the IRC presented in Fig. 4d allows us to reach a clear conclusion that the middle N3HN3 H-bond and the O2O2 vdw contact are cooperative and mutually reinforce each other, 28,92 while the upper N4HN4 H-bond is anti-cooperative to the middle N3HN3 and the O2O2 vdw contact, mutually weakening each other in the CC* and C*C (de N4HN4 /de N3HN3 /de O2O2 = 1.00/ 2.49/ at the IRC = 7.47 Bohr and Fig. 8 Profiles of (a) the distance R(H H) between the glycosidic hydrogens and (b) the a 1 (+N1H(C)H(C*)) and a 2 (+N1H(C*)H(C)) glycosidic angles along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013

11 Fig. 9 Profile of the +C4N3(C)N3C4(C*) dihedral angle along the IRC of the CC* 2 C*C tautomerisation via the DPT obtained at the B3LYP/ G(d,p) level of theory in vacuo. de N4HN4 /de N3HN3 /de O2O2 =1.00/ 2.66/ at the IRC = 6.89 Bohr) base pairs. Notably, at the IRC = 5.85/5.94 Bohr the energies of the N4HN4 and N3HN3 H-bonds become equal (7.45 kcal mol 1 ). We established that the CC* 2 C*C tautomerisation is assisted by the O2O2 vdw contact, 66,68,93 which in contrast to the canonical H-bonds exists within the entire IRC range from 7.47 Bohr to 6.89 Bohr (Fig. 6). The maximum (0.60 kcal mol 1 ) of the energy E O2O2 of the O2O2 vdw contact is attained at the IRC = 1.27 Bohr, while the minimum (0.31 kcal mol 1 ) at the IRC = 6.89 Bohr. The dependencies of the energy E O2O2 of the O2O2 vdw contact, estimated by the EML formula, 72,73 the electron density r and the Laplacian of the electron density Dr at the (3, 1) BCP of the O2O2 vdw contact on the IRC are bell-shaped, reaching their maximal values at the TS region and minimal values at the CC*/C*C base mispairs (Tables 1 and 2, Fig. 6a, b and d). Moreover, the shapes of these profiles are similar to each other, indicating a strong correlation between E O2O2, r and Dr values. This observation is in good agreement with the literature data In contrast, the d O2O2 distance between the oxygen atoms of the O2O2 vdw contact acquires its minimal values at the TS region and maximal at the CC*/C* C base mispair (Tables 1 and 2, Fig. 6e). The ellipticity e at the (3, 1) BCP of the O2O2 vdw contact has a double-well U-like profile, reaching its maximal values at those points, where the energy E O2O2 of the O2O2 vdw contact reaches minimal values and vice versa, attaining its minimal values, where the energy E O2O2 reaches maximal values (Fig. 6c and d). The behavior of e indicates that the O2O2 vdw contact is very sensitive to the dynamical behavior of the base pair and its energy is modulated by the low-frequency intermolecular vibrations of the base pair that tautomerises ,68 It should be noted that the weaker is the contact, the stronger is the modulation. The obtained sweeps of the NBO charges of the hydrogen atoms localized between the N4 and N3 nitrogen atoms along the IRC of the CC* 2 C*C tautomerisation via the DPT are presented in Fig. 7. The sharp peaks, reflecting the proton movement, are observed on the sweeps of the NBO charges exactly at key points 4 and 6 (Fig. 7). We established that the CC* base pair breathes throughout the tautomerisation process, maintaining at this its short Watson Crick geometry and propeller-like structure (Fig. 5a, c, 6e, 8 and 9). The compression of the starting CC* base mispair, which is maximally observed at the TS region, occurs due to the contraction of the distances between the N4 nitrogen (by Å), the N3 nitrogen (by Å) and the O2 oxygen (by Å) atoms (Fig. 5a and 6e). This phenomenon is also reflected by the changes of a 1 (+N1H(C)H(C*)) and a 2 (+N1H(C*)H(C)) glycosidic angles, oscillating within the range 59.5 to and 58.7 to 61.21, respectively, and of the R(H H) distance between the glycosidic hydrogens, which varies in the range to Å (Fig. 8). It is quite natural that the R(H H) distance for the CC* base pair is equal to the R(H H) distance for the C*C base pair (Fig. 8a). At this also both the +N4HN4 (171.4 to ) and +N3N3 (171.0 to ) angles significantly vary along the IRC (Fig. 5c). The +C4N3N3C4 dihedral angle, that describes the propellerlike character of the base pair, also changes during the CC* 2 C*C tautomerisation through the DPT (Fig. 9). The dependence of this angle on the IRC is non-monotonic: it lies within the range from 46.3 to Characteristically, that at the IRC = 3.32/3.51 Bohr the propeller angle of the base pair reaches maximum 52.0/52.31, respectively (Fig. 9). Physico-chemical mechanism of the CC* 2 C*C tautomerisation via the DPT Based on the analysis of the sweeps of the geometrical and electron-topological characteristics of the intermolecular H-bonds, namely on the observed spacings of the w-like crossings on the d N4H/HN4, d N3H/HN3, r, Dr and e profiles, we draw the conclusion that the CC* 2 C*C tautomerisation proceeds through the asynchronous concerted mechanism. The CC* base mispair converts into the C*C base mispair by the sequential migration of the first proton, localized at the N4 nitrogen atom of the C amino tautomer, along the N4HN4 H-bond to the N4 nitrogen atom of the C* imino tautomer. The CC* 2 C*C tautomerisation reaction has been shown to proceed via the TS, which represents itself a C + C zwitterion with a separated charge 0.62 e, stabilized by the N4 + HN4, N3 + HN3 H-bonds and the O2 + O2 vdw contact (Tables 1 and 2, Fig. 1). Then, passing the TS CC* 2 C*C, the second mobile proton, localized at the N3 + nitrogen atom of the C + protonated base, moves to the N3 nitrogen atom of the C deprotonated base. This eventually leads to the formation of the final C*C mispair involving mutagenic and canonical tautomers of the C nucleobase. Concluding remarks QM calculations combining with QTAIM analysis and the methodology of the sweeps of the energetical, electron-topological, geometrical and polar parameters were conducted in order to elucidate the tautomerisation mechanism of the biologically important CC* mismatched DNA base pair with a propeller-like structure and cisoriented N1H glycosidic bonds ( C4N3N3C4 = 32.41;C 1 symmetry) This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys.

12 formed by the amino and imino tautomers of the nucleobase via the asynchronous concerted DPT through the zwitterionic TS CC*2C*C ( C4N3N3C4 = 48.51; C 1 symmetry) into the C*C mispair. It was established that the CC*/C*C DNA base mispair is associated by the antiparallel N4HN4 (6.66 kcal mol 1 ), N3HN3 (6.47 kcal mol 1 ) H-bonds and the O2O2 vdw contact (0.33 kcal mol 1 ). The zwitterion-like TS CC*2C*C is stabilized by the parallel N4 + HN4 (13.55 kcal mol 1 ), N3 + HN3 (13.20 kcal mol 1 ) H-bonds and the O2 + O2 vdw contact (0.60 kcal mol 1 ). It was established that the CC* 2 C*C tautomerisation via the DPT is assisted by the O2O2 vdw contact along the entire IRC range. The positive value of the Grunenberg compliance constants ( and Å mdyn 1 for the CC*/C*C and TS CC*2C*C,respectively) evidences that the O2O2 vdw contact is a stabilizing closedshell interaction. The 9 key points for the CC* 2 C*C tautomerisation via the DPT were detected and comprehensively investigated along the IRC, 3 of which are stationary structures: the initial state the CC* reactant (key point 1), the TS (key point 5) and the final state the C*C product (key point 9), which is equivalent to the reactant; the 4 key points correspond to the structures, where the Laplacian of the electron density equals zero at the (3, 1) BCPs of the N4HN4/N4HN4 (Dr HN4 / Dr N4H = 0 at the key points 2/4, respectively) and N3HN3/ N3HN3 (Dr N3H /Dr HN3 = 0 at the key points 6/8, respectively) H-bonds, that is when the H-bonds become the covalent bonds and vice versa and the 2 key points correspond to the structures with the loosened N4 H N4 (the key point 3) and N3 H N3 (the key point 7) covalent bridges. Interestingly, as was noted earlier, the extrema of the first derivative of the electron energy with respect to the IRC de/dirc (well known in the literature as reaction force ) is reached exactly at key points 2 and 8. This behavior is not an individual physicochemical property of the investigated base pair. A thorough analysis of earlier results obtained by us regarding the physicochemical nature of the DPT in the H-bonded pairs of nucleotide bases 28 31,82,83 allows to state that the aforementioned feature has a general nature and does not depend on the structure of H-bonded complexes. Thus, the phenomenological approach of the reaction force 90,91 received atomistic, microstructural interpretation. Based on the sweeps of the energies of the intermolecular interactions, it was found that two intermolecular antiparallel N4HN4 and N3HN3 H-bonds are anti-cooperative and mutually weaken each other, while the middle N3HN3 H-bond and the O2O2 vdw contact are cooperative and mutually reinforce each other. It was shown that the CC*/C*C base pair is a thermodynamically and dynamically stable structure. Its lifetime is equal to s at the MP2/cc-pVQZ//B3LYP/ G(d,p) level of theory in vacuum. All 6 low-frequency intermolecular vibrations (27.4, 34.9, 49.3, 77.5, 95.8 and cm 1 )areableto develop during this period of time. The CC* 2 C*C Löwdin s tautomerisation via the DPT is the periodic and dipole-active process which occurs with frequency 6.53 MHz. Finally, the authors arrived at the biologically important conclusion that the C* mutagenic tautomer, migrating from the parent to the daughter strand of DNA, is shared with equal probability between the two DNA strands during the dissociation of the CC*/C*C mispair by the DNA polymerase. This is a direct consequence of the symmetry of the base pair which tautomerises. These observations mean that the C*C base pair can be a source of the C* mutagenic tautomer generation at the DNA replication under the condition that it would form in the active center of the DNA polymerase. Finally, we would like to note that our results have not only theoretical significance, which is important for understanding the nature of the origin of spontaneous point mutations in DNA, but are also interesting from an application point of view. It is not excluded that the C*C base mispair can be used in modern biomolecular electronics for the creation on its basis of the nanostructural bistable elements which are managed by the external electric field. 94 Acknowledgements This work was partially supported by the Science and Technology Center in Ukraine (STCU) within project No 5728 for years and by the State Fund for Fundamental Research (SFFR) of Ukraine within the Ukrainian Japanese project No F 52.4/001 for years. O.O.B. was supported by a grant of the President of Ukraine to support scientific research of young scientists for 2013 year from the State Fund for Fundamental Research of Ukraine (project No GP/F49/024) and by a grant of the President of Ukraine for talented youth for 2012 year from the Ministry of Education and Science, Youth and Sports of Ukraine. The authors thank the Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine for providing calculation resources and software. This work was performed using computational facilities of a joint computer cluster of the SSI Institute for Single Crystals of the National Academy of Sciences of Ukraine and the Institute for Scintillation Materials of the National Academy of Sciences of Ukraine incorporated into the Ukrainian National Grid. The authors sincerely thank Dr. Roman O. Zhurakivsky (Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine) and Dr. Fernando R. Clemente (Gaussian, Inc.) for their technical support of the work. References 1 R. C. von Borstel, Mutat. Res., Fundam. Mol. Mech. Mutagen., 1994, 307, K. Showalter and M. D. Tsai, J. Am. Chem. Soc., 2001, 123, C. Dohet, R. Wagner and M. Radman, Proc. Natl. Acad. Sci. U. S. A., 1985, 82, G. V. Fazakerley, E. Quignard, A. Woisard, W. Guschlbauer, G. A. van der Marel, J. H. van Boom, M. Jones and M. Radman, EMBO J., 1986, 5, Phys. Chem. Chem. Phys. This journal is c the Owner Societies 2013