How proton transfer affects the helical parameters in DNA:DNA microhelices

Abstract Proton transfer reactions are a widespread phenomenon in many areas of the life sciences and it is one of the origins of the spontaneous point mutations during DNA replication. Because of its importance, many studies have been reported on these reactions. However, the present work is the first one focused on the structural geometrical changes by double proton transfer (DPT). Thus, different Watson–Crick (WC) pairs were optimized first in a simple model with one nucleoside base pair, and in a microhelix form with three nucleoside base pairs. The canonical and few tautomeric forms were considered in DNA:DNA microhelices with A-type and B-type helical forms. The stability of these structures and how the DPT process affects the main geometrical parameters was analyzed, in particular the deformation of the helical parameters. The M06-2X DFT method was used for this purpose. The purine/pyrimidine ring in the keto form appears easier to be deformed than when it is in the enol form. The weaker WC base pair formed with mixed microhelices than with nucleobases alone and the significant deformation of the helical and backbone parameters with the DPT appears to complicate this process in microhelices. Communicated by Ramaswamy H. Sarma


Introduction
The cellular machinery shows errors during DNA replication. These errors generate mutations that affect health disorders as cancer (Srivastava, 2019). Two types of mutations appear during this DNA replication: induced mutations due to external agents, and spontaneous mutations. As an origin of these spontaneous point mutations arising in DNA (Brovarets' et al., 2012;Srivastava, 2019) has been considered the prototropic tautomerism of nucleotide bases. As the detection of the different tautomer forms appears difficult, this tautomeric assumption has been studied by different computational approaches (Danilov et al., 2005) and in some cases confirmed experimentally (Bebenek et al., 2011;Wang et al., 2011). In spite of the particularly high tautomerization barrier (around 167.2 kJ/mol) and the very slow rate of these reactions, canonical bases can be tautomerized (Brovarets & Hovorun, 2010;Furmanchuk et al., 2011;Podolyan et al., 2003). Two alternative ways of mutagenic tautomers formation have been discussed in literature: (i) water assisted tautomerization by bulk aqueous solution (Danilov et al., 2009;Furmanchuk et al., 2011), by microhydration (Kim et al., 2007) or by an individual interacting water molecules (Fogarasi, 2008;Hu et al., 2005) and (ii) L€ owdin's tautomerization consisting in double proton transfer (DPT) along two intermolecular hydrogen bonds of complementary DNA base pairs (L€ owdin, 1963). The first mechanism (i) is the most important and studied ones since it can principally explain the tautomerization of Nucleic Acid Bases (NABs) in both DNA and incoming nucleotides during DNA biosynthesis. It is based on the fact that water molecules are capable of binding to proton-acceptor and proton-donor sites in nucleobases (Furmanchuk et al., 2011). However, the second mechanism (ii) is exclusively related to the DNA/RNA replication, and it has been less studied. Thus, we focus the attention on this second mechanism in the present work.
Because the point mutagenic single proton transfers (SPTs) is less favorable than the DPT mechanism, due to the electroneutrality of the Watson-Crick (WC) pairs, the present manuscript is focused only on DPT. A wide range of theoretical studies on this DPT mechanism has been reported in detail with nucleobases in the tautomerization of the WC base pairs guanineÁcytosine (GÁC$G Ã ÁC Ã ) (Brovarets' et al., 2019) and adenineÁthymine (AÁT) (Brovarets' & Hovorun, 2015b), and in the mismatched DNA base pairs CÁT (Brovarets' & Hovorun, 2013, 2015d, TÁT Ã , AÁC and AÁC Ã (Brovarets' & Hovorun, 2015c), G Ã ÁT and GÁT Ã (Brovarets' & Hovorun, 2015a) and in the long AÁG , 2015d and GÁG Ã , where mutagenic tautomers of the bases are marked with an asterisk. Among these irregular DNA base pairs that cause point mutations, GÁT and AÁC are currently the best studied (Bebenek et al., 2011;Wang et al., 2011). All these studies show the great biological interest of these mispairs. Thus for example, the formation of G Ã ÁC Ã pair can cause the formation of the G Ã ÁT and AÁC Ã mispairs in the next round of DNA replication leading to point mutations in DNA (Brovarets' et al., 2019).
Most of these studies on DPT are on nucleobases. Thus, in the present work, we consider of interest to carry out the DPT study on nucleosides and on small microhelices, and to compare the results with those obtained with nucleobases. It is important to carry out this study because nucleobases are planar, but the purine/pyrimidine rings of nucleosides are not-planar and this non-planarity increases in the nucleotide form of a microhelix (Alcolea  and how the DPT is affected by this non-planarity is of particular interest. As first step, the present study is only focused on the structural and energetic of the DPT in the biologically important dAÁT and dGÁdC WC base pairs with nucleosides and in different combinations with them in three microhelices with the help of DFT methods. In addition, the mismatched base pairs with nucleosides dGÁT Ã (and dG Ã ÁT), and dAÁdC Ã (and dA Ã ÁdC) were also analyzed. The structural characteristics of this DPT in nucleosides, as well as in microhelices, have not yet been reported from quantum chemical studies, which is one of the purposes of the present work.
Another aim of interest is to know how much the microhelix is deformed by DPT. Because the activity of DNA polymerases and repairing enzymes depends upon the changes in the base-pair geometry, therefore, the importance of understanding the deformation of the different microhelix parameters by this DPT process and how the strands of the microhelix change. Although this study is carried out in gas phase, these microhelices have the ability to preserve the conformation under the influence of a solvent or counter-ions (Alcolea Zubatiuk et al., 2013). Therefore, only slight changes of our results are expected under these conditions.

Computational methodology
Theoretical calculations were carried out using the second-order Møller-Plesset perturbation theory (MP2) ab initio method and the meta-generalized gradient approximation M06-2X (Zhao & Truhlar, 2008b) Density functional (DFT) method. The Popl es 6-31G(d,p) and 6-311 þ G(d,p) basis sets were used for this purpose through the Gaussian16 program package (Frisch et al., 2019) running in the Computational Center of the Complutense University of Madrid. Standard parameters have been used under the UNIX version of the program. The MP2 method was used for the optimization of the nucleosides and for all the WC base pairs with nucleobases, but on larger systems it could not be used due to computer memory requirements. The Minnesota functional M06-2X was selected for the fully optimization of all the WC pairs with nucleosides and the double stranded DNA-like microhelices (or mini-helixes). It is because in previous calculations by us on similar systems (Alcolea Palafox, 2019; Alcolea  or by other authors (Zubatiuk et al., 2013) it shows the best results. Moreover, it is the best choice among other meta-generalized gradient functionals to examine dispersion-bound systems (Riley & Hobza, 2011;Riley et al., 2010), in particular nucleobase stacking (Churchill & Wetmore, 2011;van Mourik, 2009;Zhao & Truhlar, 2008a). An excellent work on the DNA base stacking uracil/uracil and thymine/thymine (Hunter & van Mourik, 2012) indicates the excellent agreement in the interaction energy between M06-2X and CCSD(T)/CBS values. The Berny algorithm was used for the optimization process under the standard convergence criteria. The default fine integration grid was utilized.
Only two types of microhelices (Alcolea Palafox, 2019) were optimized and considered in the present work. They were calculated with a global negative charge of À4. The ends of the backbone chain in H5 0 -1 and H3 0 1 was oriented to avoid the formation of spurious intramolecular H-bonds, and therefore, they were not substituted by methyl groups as in related optimizations by other authors (Zubatiuk et al., 2013).
The present work is the first comprehensive DFT study of the effect of the DPT in three WC trideoxyribonucleoside diphosphate homo-and hetero-polymers. These small microhelices are large enough to realistically mimic the structure of DNA (Zubatiuk et al., 2013). To guarantee that both strands of the helix correspond to the same A-type or B-type, a previous optimization with the RNA:RNA helices was carried out. Further removing of the 2 0 -OH groups of both strands lead to these two types of DNA:DNA helixes. This procedure gives rise to noticeable more stable helixes (higher negative energy).

Calculation of the interaction energies
The interaction energies have been calculated in the WC pairs with the nucleosides in the canonical and in the tautomeric forms, and in several microhelices with the furanose ring of the nucleotide as a b-D-2 0 -deoxyribose (DNA). The values obtained in each nucleoside pair were corrected for the mathematical artefact of basis set superposition error (BSSE) (Boys & Bernardi, 1970) through the counterpoise procedure (Sordo, 2001), which is described elsewhere (Alcolea Palafox et al., 2009;Danilov et al., 2006;Hunter & van Mourik, 2012;Mentel & Baerends, 2014;Zubatiuk et al., 2013). The calculations were performed using the 'Scan' and 'Counterpoise' keywords in Gaussian16 program package (Frisch et al., 2019). The total CP corrected interaction energy, DE CP AB between nucleoside A ( pyrimidine) and nucleoside B ( purine) was obtained according to the following relation: where the electronic interaction energies E int have been computed at the M06-2X/6-31G(d,p) level of theory as the following relation, In this expression, E AB AB ðABÞ represents the total calculated electronic energy of the entire base pair system (AB), and E AB A AB ð Þ (or E AB B AB ð Þ) corresponds to the electronic energy of the isolated subsystem A (or B) in the whole system (AB). The BSSE correction is included in both energies (1) and (2). In the microhelices, these isolated subsystems A or B correspond to each strand of the helix. The deformation energy E def (AB) was described as: In the above expression, the parentheses indicate whether the calculations were done at the optimised molecular geometry of the monomer form (A or B) or of the entire system (AB). The superscripts indicate whether the computations were carried out with the basis set of monomer (X), or the entire system, and the subscripts denote the molecular system studied.

Characteristic conformational parameters in nucleotides
The atomic description in the microhelix, and the conventional notations used for the exocyclic (v, f, a, b, c, d, e) and endocyclic ( 0 to 4 ) torsional angles appear described in the Saenger's book (Saenger, 1984) and reported in many works . The labeling of the atoms is included in Schemes 1 and 2. The subscripts (-1, 0 and 1) on the atoms correspond to the base pair plane of the microhelix. The definition of these characteristic parameters can be summarized as follows: (i) The torsional angle v(O4 0 -C1 0 -N1-C2) is known as the glycosylic angle and it is the most important parameter to describe the relative position of the nucleobase related to Scheme 1. Chemical structure and labeling of the atoms in thymidine (T) and 2 0 -deoxyadenosine (dA) nucleosides, and in guanine and cytosine nucleobases and notation used for the description of the exocyclic and endocyclic torsional angles. the furanose ring, and namely as syn, anti and high-anti forms. (ii) The skeletal angle f(C3 0 -1 -O3 0 -1 -P 1 -O5 0 ) (Alcolea Palafox, 2019) describes the orientation of furanose-phosphate backbone and the helical twist. (iii) The torsional angle a(O3 0 -1 -P 1 -O5 0 -C5 0 ) defines the position of the O3 0 -1 oxygen atom (Alcolea Palafox, 2019) in the phosphate moiety. (iv) The exocyclic angle b(P 1 -O5 0 -C5 0 -C4 0 ) determines the orientation of the phosphate group related to the furanose ring, which appears rotated to reduce non-bonded interactions.
(v) The torsional angle c(O5 0 -C5 0 -C4 0 -C3 0 ) describes the orientation of O5 0 oxygen related to the furanose ring, which appears rotated to facilitate the weak/very weak intramolecu-lar H-bond of O5 0 with H6 of the pyrimidine nucleobase or with H8 of the purine nucleobase. (vi) The exocyclic angle d(C5 0 -C4 0 -C3 0 -O3 0 ) is the main angle that is related to the symmetry of the furanose ring. (vii) The torsional angle e(C4 0 -C3 0 -O3 0 -P 2 ) describes the orientation of the phosphate group related to the furanose ring. It contributes to the microhelix helical twist. The exocyclic angles b and e generally appear in trans-form in the helix. (viii) The pucker P (pseudorotation phase angle) determines the symmetry of the furanose ring, and it is described as: Scheme 2. Definition of the torsional angles for the polyribonucleotide chain in strand I and labeling of their atoms.
where 0 to 4 correspond to the endocyclic angles (Saenger, 1984) of the sugar ring. The maximum torsional angle (degree of pucker), m max , appears also important and it has been defined as: Its value is related to the flexibility of the furanose ring. That is, a large value corresponds to a high flexibility.

Main characteristic parameters of the helix
The optimized microhelices are formed by two strands (I and II) and have been calculated at the M06-2X/6-31G(d,p) level in a simplified model with three nucleotide base pairs. It is expected that the calculated values with these microhelices can be closely to those in a long helix. Previous studies (Alcolea Palafox, 2019; Alcolea  carried out by us on microhelices have shown that this simplified model is appropriate for the present work. In this microhelix, the DPT process is only simulated in the central fragment, i.e., WC base pair in plane n (Scheme 1). Therefore, only the optimized parameters obtained through this nucleotide pair are included in the Tables 1-7.
The helical structure appears mainly described (Alcolea Lavery et al., 2009;Saenger, 1984) through several sets of parameters that define: (i) the individual conformational angles (exocyclic and endocyclic) of the nucleoti- Table 1. Calculated characteristic parameters of the most stable conformers of thymidine (T), 2 0 -deoxycytidine (dC), 2 0 -deoxyadenosine (dA) and 2 0 -deoxyguanosine (dG) nucleosides in the anti-form at the MP2/6-31G(d,p) level. Energy increments (DE) are in kJ mol À1 , the exocyclic torsional angles, the pseudorotational angle P and the maximum torsional max . are in degrees. a Symmetry (S), the 4 3 T 3 notation corresponds to the C(4 0 )-exo-C(3 0 )-endo twist conformation.  The notation used for the intermolecular H-bonds ‹ and › is in accordance to that reported in reference (Alcolea Palafox, 2019). Bond lengths are in Å, and bond angles and torsional angles are in degrees. a Figure 3. b The furanose ring in I corresponds to the pyrimidine nucleoside, and II to the purine nucleoside. Ã Mutagenic tautomers of the bases. des in the helix, (ii) the translation and rotation of each base pair in the helix (Sy, Sx, hp, u o , r) and (iii) the stacking of these base pairs (Dz) and their helicoidal forms (d, R, g, x). The notation used here for the characterization of the microhelices only refers to one of the strands. Thus, for example: the DNA:DNA microhelix: with 2 0 -deoxyadenosine (dA) and thymidine (T) in the first strand is represented by: , and the microhelix: with dA and 2 0 -deoxycytidine (dC) in the first strand and with T and 2 0 -deoxyguanosine (dG) in the second strand is represented by: 5 0 -dA dC dA-3 0 And so on, following the same way in the notation of all the microhelices. Counting of nucleotides in these microhelices was carried out from top to bottom, i.e., following the O5 0 !O3 0 direction.

Types of microhelices
In the DNA:DNA double-helical, the A-and B-DNA biological forms are considered to be the most significant. Thus, whereas the B-DNA prevails under physiological conditions (Neidle, 2008;Yurenko et al., 2016) and participates in most of biochemical processes in vivo because its extensive structural heterogeneity (Leslie et al., 1980), the A-DNA is known to be more conformationally homogenous (Maehigashi et al., 2012), which points to its role in preserving the genetic material (Yurenko et al., 2016;Zhurkin et al., 1975). In our calculations, two types of microhelices appear as the most stable (Alcolea Palafox, 2019), and labeled as A-type and B-type. This notation is in agreement with that of A-and Btypes polynucleotide double helices (Saenger, 1984), where Atype appears in the C3 0 -endo form with P1ÁÁÁP2 interatomic distance (Saenger, 1984) of 5.9 Å (6.340 Å in the microhelix 5 0 -TTT-3 0 , Table 7) and B-type appears in the C2 0 -endo form with P1ÁÁÁP2 ¼ 7.0 Å (7.088 Å in the microhelix 5 0 -TTT-3 0 ). The torsional angle d was calculated with a value approximately 130-140 in B-type microhelices (134.8 in strand I of 5 0 -TTT-3 0 ), and approximately 80-85 in A-type microhelices.
In RNA strands, A-and B-types correspond to the two main possible orientations of the hydroxyl hydrogen H2 0 (O2 0 ) n of the sugar ring (Alcolea Palafox, 2019): to be intramolecular Hbonded to O4 0 (n þ 1) of the adjacent nucleotide (A-type), or to be H-bonded to O7 0 (n þ 1) of the phosphate moiety (B-type). Such possible two H-bonds contribute in the stabilization of these helices. A-type corresponds to the O2 0 -H2 0 (n) ÁÁÁO4 0 (n þ 1) H-bond between contiguous nucleotides of the same strand, and the nucleobase ring is in high-anti orientation relative to the furanose ring. B-type corresponds to the O2 0 -H2 0 (n) ÁÁÁO7 0 (n þ 1) H-bond between contiguous nucleotides of the same strand, Table 4. Optimized bond lengths (in Å) determined in the pyrimidine and purine rings of several DNA:DNA simulated microhelices with three nucleotide base pairs.  and the nucleobase ring appears in anti-orientation related to the furanose ring. Microhelices B-type appears always remarkable more stable than A-type, mainly as a result of an intramolecular Hbond stronger in B-type (H2 0 (n) ÁÁÁO7 0 (n þ 1) ¼ 1.627 Å in strand I of 5 0 -UUU-3 0 ) than A-type (H2 0 (n) ÁÁÁO4 0 (n þ 1) ¼ 2.076 Å in 5 0 -UUU-3 0 ) (Alcolea , and because the anti-orientation (B-type) appears more stable than the high-anti orientation (A-type).
In DNA strands, the hydrogen H2 0 (Scheme 1) substitute to the O2 0 atom of RNA strands in the way that H2 0 has the same orientation in A-and B-types that in the related RNA strands, and with the same orientation of the purine/pyrimidine rings (anti and high-anti, respectively) that in RNA strands, and with the same orientation of the furanose ring (2 0 -endo and 3 0 -endo, respectively) that in RNA strands.

Characteristic parameters in the microhelices
A large number of parameters have been described (Diekmann, 1989) to explain the geometric relations between bases in a helix. In addition, other definitions of local and global axes have also been used (Dickerson, 1989;Neidle, 2008). Only few of these parameters characterized for individual base pairs (translational and rotational) and for base stacking have been calculated and discussed in the present study. The definition of three of them is as follows: i. The rise parameter (Dz) appears described as the distance between bases in stacking form. It was calculated in the purine and pyrimidine rings according to reference (Alcolea Palafox, 2019). In strand I, Dz -1 corresponds to the distance between the geometric center of the nucleobase ring of plane (n -1) and plane n (Scheme 2), while Dz 0 refers to the planes n and n þ 1. Because the chain growing of strand II is in opposite direction of strand I, the plane (n -1) in strand I corresponds to the plane (n þ 1) in strand II and vice versa, the plane (n þ 1) in strand II refers to the plane (n -1) in strand I. ii. The propeller twist h p is defined as the dihedral angle between individual base planes. It was calculated only between the purine and pyrimidine rings of plane n, that in the present study it corresponds to the dihedral angles of the T/dA and dC/dG nucleobase rings. It can be obtained roughly through the torsional angle u 0 iii. The inclination angle (g) of the base pair was measured relative to the helical axis passing through O o , and it was calculated as g qO o C8 dA=dG 0 : The geometric points q and O o (centrum of the microhelix axis) were determined according to reference (Alcolea Palafox, 2019).

Conformational analysis of the natural nucleosides
A previous conformational analysis of thymidine (T), 2 0 -deoxycytidine (dC), 2 0 -deoxyadenosine (dA) and 2 0 -deoxyguanosine (dG) nucleosides was carried out. Thus, for example, in Table 5. Torsional angles in degrees of the purine and pyrimidine ring planarity, and several structural parameters optimized in both strands of DNA:DNA microhelices with three nucleotide base pairs. Microhelix type Pyrimidine ring Purine ring thymidine 34 conformers were calculated at the MP2/6-31G(d,p) level and a similar number of conformers were obtained in the other nucleosides. The large range of values of the exocyclic and endocyclic torsional angles in these conformers indicates the flexible nature of these nucleosides, in accordance to Shishkin et al. (1999). This feature is also confirmed by the low-lying vibrational modes (with wavenumbers below 200 cm À1 ) responsible for the motion of sugar and base with respect to each other as well as the collective vibrations involving deformation of both the sugar and the base (Shishkin et al., 2000a).
Only the values of the main characteristic structural optimized parameters of the most stable conformers in the anti form of these nucleosides at the MP2/6-31G(d,p) level are collected in Table 1, as well as the calculated relative energies and dipole moments (m) of them. Only two conformers are included in dC, dA and dG nucleosides and four conformers in T. Previous results with few conformers have also been reported by other authors (Shishkin et al., 2000b). The notation used for them is that reported elsewhere (Bloomfield et al., 2000;Saenger, 1984;Yurenko et al., 2011). Table 6. Exocyclic torsional angles (in degrees) calculated in both strands of the DNA:DNA microhelices, and the pseudorotational phase angle P.

Strand
Type Values in italic type corresponds to the 6-311 þ G(d,p) basis set.  The NBO atomic charges correspond to the N3 T,dC , O4 T (N4 dC ), N1 dA,dG and N6 dA (N2 dG ) atoms. The nucleobase in plane n is a pyrimidine ring in strand I and a purine ring in strand II. Values in italic type corresponds to the 6-311 þ G(d,p) basis set.  The conformation of the sugar ring is highly dependent on the nature and arrangement of the nucleobase (Shishkin et al., 2000b). Therefore, conformers AI and AII are C3 0 -endo and leads to microhelices A-type, while conformers BI and BII are C2 0 -endo and leads to microhelices B-type. Conformers BI are more stable than AI in all the nucleosides, except dC. AI and BI forms are stabilized by the C6-H6ÁÁÁO5 0 (in pyrimidines, Figure  1) and C8-H8ÁÁÁO5 0 (in purines) non-traditional intramolecular H-bonds. Although this H-bond is rather weak, it is considered to be a real H-bond of CHÁÁÁO type (Yurenko et al., 2011), with an energy of around 4 kJÁmol À1 . With these AI and BI forms was building the DNA:DNA microhelices of the present work.
The two most optimum conformers of T (BI and BII forms, Figure 1) appear with the sugar orientation in the C2 0 -endo form ( 2 E). The global minimum is in this orientation, with a difference of only 3.6 kJ/mol related to AI of the C3 0 -endo form ( 3 E), Table 1. However, in DNA growth, only the incoming nucleotides with the C3 0 -endo conformation appear to help position and correctly orient the phosphate group (Heuberger et al., 2015;Yokoyama et al., 1985) to react with the attacking 3 0 -OH group of the primer. Transition from 2 E to 3 E can be done by a lengthening of the C1 0 -C2 0 and C2 0 -C3 0 bonds and the corresponding shortening of C3 0 -C4 0 (Shishkin et al., 2000b), and for this purpose, the glycosyl bond N-C1 0 appears more flexible to facilitate the transition in purines than in pyrimidine nucleosides. Therefore, both 2 E and 3 E forms are of interest and they are studied in the B-type and A-type microhelices, respectively.
In individual nucleobasis and in their base pairs, the purine and the pyrimidine rings are calculated at the M06-2X/6-31G(d,p) level as full planar. However, in nucleosides these rings show a slight out-of-planarity, especially in the pyrimidine rings, in accordance to their large flexibility. This slight non-planarity is expected to have an influence in the DPT.
The large values of m are due to their large polarizability, which is in general slight larger as nucleoside than as nucleobase. For example, the values of m in the nucleoside T, Table 1, are noticeable larger than 4.858 D of its nucleobase.

Tautomerism in the natural nucleosides
The nucleic acid bases and their derivatives exhibit the phenomenon of tautomerism, which has an especial role in mutagenesis of DNA. A large amount of work has been performed on the tautomerism of nucleic acid bases, using both theoretical Brovarets', Tsiupa, Dinets, et al., 2018;Gould et al., 1995;Mohamed et al., 2009;Mohammadi & Ramazani, 2016) and experimental (Chahinian et al., 1998;Hendricks et al., 1998) approaches, and the effect of water in this tautomerism (Hu et al., 2005;Rejnek et al., 2005). However, the tautomerism of the natural nucleosides has been less studied (Alcolea Palafox & Iza, 2010). Thus, a previous study by us of the different tautomeric forms of T, dC, dA and dG was carried out. In this tautomerization process, the purine/pyrimidine ring structure displays a regular change, where two bonds of the purine/pyrimidine rings were lengthened, whereas the other four were shortened. Furthermore, the lengthening bonds were those opposite of the transferred proton in all tautomers. Thus for example, the C ¼ O bond that receives a proton was noticeable lengthened, while the C-NH 2 bond that looses the proton was shortened (Hu et al., 2005).
In the isolated state of the nucleosides under study several tautomer forms were optimized and identified, although only the three most stable ones were included in Figure 2. Notation of these tautomers is in accordance to that reported in refs. (Alcolea Palafox, 2017;Alcolea Palafox & Iza, 2010). The relative energies of these tautomers appear related to the dipole moment (m). Therefore, the most stable keto/amino tautomer has a higher value of m than the corresponding most stable enol/imino form. In T and dG it can be explained by the shift of the carbonyl C ¼ O group to the C-OH group, which decreases m. The stability of these keto/ amino tautomers will be favored in water environments. However, the base pair recognition pocket of DNA   polymerase is substantially hydrophobic which can favor the mutagenic enol/imino tautomers. In the nucleosides under study, the DPT was performed in the keto/amino form leading to its most stable enol/imino tautomeric form. Namely, tautomer T3 in thymidine, tautomer C3b in dC, tautomer A2 in dA and tautomer G2 in dG, Figure 2.

Proton transfer in the canonical WC pairs of the natural nucleosides
The effect of the DPT was studied in the dAÁT and dGÁdC base pair with the natural nucleosides. Among the four classical configurations with biological significant, the base pairs with WC geometry was only studied here. These pairs were established with the best conformer of the canonical form, and with the furanose ring in C3 0 -endo as b-D-2 0 -deoxyribose (DNA), and as b-D-ribose (RNA) (Supporting Information). The optimized geometrical parameters of these base pairs were compared to those obtained when the DPT is performed. A comprehensive comparison of the most important structural parameters of only few WC pairs with the b-D-2 0 -deoxyribose ring is shown in Table 2, while the values obtained in the WC pairs with a b-Dribose ring are collected in Table S1 (Supporting Information). The optimum structure obtained in the dAÁT and dGÁdC base pairs with the furanose ring in C3 0 -endo is shown in Figure 3, as well as the DPT optimized structures with these base pairs. The notation used for the intermolecular H-bonds is from reference (Alcolea Palafox, 2019). The non-classical ¼ O2 T ÁÁÁ H-C2 dA interaction fi of the dAÁT WC pair appears rather weak, but it has been classified as a true H-bond (Yurenko et al., 2011) and it assists to stabilize the structure. For this reason, their values were included in Table 2. The main effects observed in these WC pairs were the following: i. In the WC pair formation, the small non-planarity of the pyrimidine ring is slightly increased, especially in the atoms involved in intermolecular H-bonds. However, the WC pair formation little affect the very small non-planarity of the purine ring. It is in accordance to the slightly more flexible pyrimidine than purine rings. Therefore, only the main torsional angles of the pyrimidine ring are collected in Table 2, columns second-fifth. ii. The intermolecular H-bonds ‹ and › of the base pair dGÁdC with nucleosides appear slightly weaker than with nucleobases (1.889 Å and 1.751 Å, respectively), although H-bond fi is slightly stronger than with nucleobases (1.898 Å). This weakening with the base pair dGÁdC is in accordance to calculated interaction energy values slightly lower with nucleosides than with nucleobases and to that reported in related systems (Alcolea Palafox, 2019). When the DPT occurs in nucleosides (  (Brovarets' et al., 2019). iii. In the dA Ã ÁT Ã base pair the proton transferred from dA to O4 T , the (O4H) T Ã group, appears weakly bonded, r(O4-H) T Ã ¼ 1.081 Å vs. 1.020 Å when this proton is bonded to -NH 2 of dA. By contrast, in the dGÁdC base pair the proton transferred from the amino group -NH 2 of dC to O6 dG appears stronger bonded, r(O6-H) dG Ã ¼ 0.990 Å. Thus, it is expected that this dGÁdC base pair could cause point mutations in DNA. However, an accurate study with nucleobases (Brovarets' et al., 2019) indicates that, although this L€ owdin's base pair satisfies all the essential requirements for point mutations, its lifetime appears to be much shorter than the period of time necessary for the replication machinery to forcibly dissociate a base pair into their nucleobases during the DNA replication (Brovarets' et al., 2019). It is noted that in the tautomeric AÁT WC pair with nucleobases (Brovarets' & Hovorun, 2015e) the reverse barrier has been reported to be absent, and with a small value in the GÁC pair. iv. An increment in the C1 0T,dC ÁÁÁC1 0dA,dG distance between the nucleosides and of the opening angle r (Alcolea Palafox, 2019) (ca. 3 in the N3-H T,dC ÁÁÁN1 dA,dG angle) is also observed by the DPT. However, the geometry of the furanose ring appears little affected by the DPT process. v. The dC nucleoside appears with slight different behaviour against DPT as compared to T because of its three intermolecular H-bonds with dG. Thus, in the dGÁdC WC pair the DPT noticeable affects the propeller twist angle hp between the base pair planes with a change of 10.5 , while in the dAÁT pair hp is little changed. Moreover, in the bond lengths of the pyrimidine ring the effect of the DPT with dC is opposite to that with T. The DPT with dC increment the p-delocalization and the aromaticity of the pyrimidine ring while with T the aromaticity is decreased, in accordance to that reported with dinucleotides (Karabı yık et al., 2014). vi. In the dAÁT WC pair formation, the deformation energy (E def ) of the pyrimidine T is noticeable higher than of the purine dA, Table 3. By contrast, in the dGÁdC pair the deformation energy is lower in the pyrimidine dC than in the purine dG. The DPT noticeable increment the E def values, with the exception of dC. Among the nucleobases, the proton H-bonded to N3 in T Ã , (N3-H) T Ã , leads to the maximum deformation of the ring. The interaction energy values in the dGÁdC WC pair are noticeable higher than in the dAÁT pair because of its three intermolecular Hbonds. The CP corrected interaction enegy DE CP AB has a lower negative value in the dG Ã ÁdC Ã pair than in dGÁdC, that is, the DPT noticeable reduces the base pairing stabilization in dGÁdC pair and by contrast it is increased in dAÁT pair.

Proton transfer in the tautomeric forms of the WC pairs
Spontaneous point mutations in DNA can occur through transition (AÁC and GÁT) and transversion (CÁC, CÁT and GÁA) mismatches. Because the large deformation of the base pairs with transversion mismatches and their lower probability of occurring, they were not studied here. In E. coli, the transition mismatches appear to be well repaired by the cellular machinery, but transversion mismatches are not (Cognet et al., 1991). The effect of the DPT in the transitions mismatches has been well studied with nucleobases (Brovarets' & Hovorun, 2015a, 2015cDanilov et al., 2005), but in the  present work they were studied with nucleosides, involving the main mutagenic tautomeric forms: the enol form T3 of T and G2 of dG, and the imino form A2 of dA and C3b of dC, Figure 2. That is, the mismatches: dGÁT Ã $ dG Ã ÁT and dAÁdC Ã $ dA Ã ÁdC, Figure 4 (tautomers are marked with an asterisk). The main structural parameters of the WC pairs with these tautomers are collected in Table 2. The DPT tautomerization with nucleobases of the wobble wGÁT DNA base mispair into the wG Ã ÁT Ã mismatch has been reported to be not mutagenic (Brovarets' & Hovorun, 2015a), and therefore, it was not studied in the present work. In addition, the microhelix with this base mispair appears noticeable deformed.
The effect of the DPT on the geometric structure of these WC DNA base mispairs with nucleosides has not yet been studied. The dAÁdC mispair with WC geometry is of special interest because it has been discovered experimentally in the recognition pocket of the DNA polymerase (Brovarets' & Hovorun, 2015c;Wang et al., 2011). Furthermore, this structure fits perfectly within the dimensions of the DNA double helix, thus, preserving the geometry with the correct canonical base pairs. In addition, the AÁC Ã mispair with nucleobases has been reported to be an active player (Brovarets' & Hovorun, 2015c) of point mutational events and it appears successfully dissociated by the replication machinery into the A and C Ã nucleobases. By contrast, the A Ã C mispair with nucleobases appears out of the replication machinery and only it plays the role of a provider of the AÁC Ã mismatched in DNA that is synthesised. Hence, the tautomerization of the biologically important dAÁdC Ã mismatched DNA base pair with nucleosides, formed by the amino tautomer of dA and the imino mutagenic tautomer of dC was optimized here. The DPT leads to the imino mutagenic tautomer of dA Ã and the amino tautomer of dC, the dA Ã ÁdC mispair. In this tautomerization process dAÁdC Ã $ dA Ã ÁdC the limiting stage with nucleobases has been reported to be (Brovarets' & Hovorun, 2015c) the final proton transfer H6 along the N4 dC Ã ÁÁÁH6-N6 dA intermolecular H-bond ‹, Figure 4, in accordance to our results in nucleosides with a longer distance N4 dC Ã ÁÁÁH6 dA (1.944 Å) than N3-H dC Ã ÁÁÁN1 dA (1.756 Å), and with a stronger H6-N6 dA bond (1.028 Å) than N3-H dC Ã (1.050 Å). In this mismatched, all three H-bonds appear cooperative and mutually reinforcing, as reported in nucleobases (Brovarets' & Hovorun, 2015c). However, the H-bond/contact fi is very weak (Table 3) and slightly weaker than with nucleobases to be considered in this case as a true H-bond.
The base mispair dGÁT Ã involving the enol mutagenic tautomer of T and the keto tautomer of dG is plotteed in Figure 4. Tautomerization of this base mispair with nucleobases has been reported (Brovarets' & Hovorun, 2015a) to occur through the asynchronous concerted DPT along two antiparallel ‹ and › H-bonds and assisted by fi. Our results with nucleosides indicate that the H-bonds ‹ and fi are almost parallel with a deviation of 1.1 , and it is only 5.7 between ‹ and ›. Conversely, it has been reported (Brovarets' & Hovorun, 2015b) that the GÁT Ã mismatch with nucleobases is short-lived, and therefore, it appears to escape of the DNA replication machinery by rapidly transforming into the G Ã T mispair which plays an important role in the spontaneous point mutagenesis (Brovarets' & Hovorun, 2015b). Our results indicate that the dGÁT Ã mispair with nucleosides appears with larger E def and stronger Hbonded than the dG Ã ÁT and the dAÁdC Ã mispairs, and with higher CP-corrected interaction energy, Table 3.
The calculated CP corrected interaction energy indicates that the DPT noticeable reduces the base pairing stabilization in the dGÁT Ã mispair and by contrast it is increased in the dAÁdC Ã mispair.

Proton transfer in the canonical forms of the WC pairs with three nucleotide pairs
Although many helical combinations with nucleosides are possible only few of them were studied here. Thus, three DNA:DNA microhelices were optimized in a simple model with three nucleoside base pairs, and with three combinations in strand I of T or dC in plane n, and T or dA in planes n -1 and n þ 1 (Scheme 2). In strand II appears the corresponding nucleosides. The DPT was carried out only in the base pair of plane n, highlighted with sticks in Figure 5. The microhelices studied were: (i) the 5 0 -TTT-3 0 with only pyrimidines in strand I and purines in strand II, and (ii) the 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 with mixed pyrimidines and purines in both strands. Two main types of microhelices were analyzed in detail depending on the furanose ring orientation, in the C3 0endo form (A-type) or in the C2 0 -endo (B-type) (Alcolea . Microhelices B-type appears more stable than A-type and with higher dipole moment, Table S2 (Supporting Information). The C2 0 -endo orientation in Btype leads to longer distances between the successive phosphate groups of each strand than in A-type, and to an anti-orientation of the nucleobase (v angle around À120 and À140 ). In A-type it is in high-anti orientation (v angle ca. À160 ). The importance of the A-type microhelices is that in the terminal nucleotide of a primer the C3 0 -endo orientation of the furanose ring appears to facilitate the attack by an activated monomer (Heuberger et al., 2015;Yokoyama et al., 1985).
The final optimized structure in two A-type microhelices is shown in Figure 5. In them, the DPT has been simulated with the particular interest of interpreting the geometric changes in the helix. Several bond lengths, bond angles and intermolecular angles of interest are summarized in Tables  4-7 and Tables S2 and S3 (Supporting Information). The use of a basis set augmented by diffuse functions, such as 6-311 þ G(d,p), only show significant effect in the helical parameters of the B-type microhelix 5 0 -dATdA-3 0 . The following features were mainly observed in these microhelices by effect of the DPT: i. Two main factors appear to contribute to the stabilization of the helix, namely base pairing H-bonds and stacking interactions between parallel layers. The DNA double helix structure is little destabilized by the DPT: it has a small value in 5 0 -TTT-3 0 (52.4 kJ/mol in A-type and 41.9 kJ/mol in B-type) and in 5 0 -dATdA-3 0 B-type (52.9 kJ/mol), and slightly smaller in 5 0 -dAdCdA-3 0 (34.1 kJ/mol in A-type and 27.3 kJ/mol in B-type). The smallest destabilization appears in 5 0 -dATdA-3 0 A-type with only 13.5 kJ/mol. ii. In the 5 0 -TTT-3 0 microhelix, a noticeable lengthening in the intermolecular H-bond ‹, about 0.15 Å (Table 5) is observed as compared to the WC pair with only one nucleoside (Table 2), and by contrast a large shortening of H-bond ›. This anti-cooperative effect of the Hbonds ‹ and › has been studied by other authors (Brovarets' & Hovorun, 2015b). However, in the mixed microhelices 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 both Hbonds ‹ and › are lengthening, as compared to one nucleoside pair alone or one nucleobase pair. That is, the tautomerism by the DPT mechanism appears difficulted when the optimized model is a microhelix instead of a single nucleoside pair or a nucleobase pair. The DPT has a very strong effect in the intermolecular H-bonds ‹ and › with a remarkable shortening of its value.
The intermolecular H-bonds between the two stands show strong linearity in both RNA:RNA (Table S4 Supporting Information) and DNA:DNA microhelices. This linearity can be observed through the N3 -H T/ dC ÁÁÁN1 dA,dG angle. The DPT reduces this linearity in the 5 0 -TTT-3 0 microhelix, and it has a different behavior in the other microhelices. iii. A slight lengthening of the N3-C4 bond length in the pyrimidine ring (N1-C2 in the purine ring) and shortening of C2-N3 (pyrimidine) and N1-C6 (purine) is observed as compared to the WC with only one nucleoside pair. The DPT increments this lengthening, Table 4. The bond angles of the nucleobase ring are little affected by the DPT. iv. The microhelix 5 0 -dATdA-3 0 shows two intramolecular H-bonds between the base pairs of the planes (n) and (n þ 1), Fig. 6. These H-bonds involve the amino group of dA and the carbonyl C4 ¼ O group of T. That is, the N6-H6 nþ1 dA ÁÁÁO4 T n H-bond in strand I and the N6-H6 n dA ÁÁÁO4 T nÀ1 of strand II. This inter-plane H-bond of strand II is slightly stronger than that of strand I and it leads to a noticeable deformation of T and thus in the planarity of the base pair of plane (n þ 1) with an increment in its propeller twist h p . Only this 5 0 -dATdA-3 0 microhelix in both A-type and B-type shows these interplane H-bonds. Although in the 5 0 -TTT-3 0 microhelix and especially in 5 0 -dAdCdA-3 0 of B-type, these interplane H-bonds also appear, but very weak. DPT noticeably weakens these interplane H-bonds. v. In the microhelix 5 0 -dAdCdA-3 0 the ring aromaticities of both dC and dG nucleosides of the pair in plane n increase throughout DPT, while in the 5 0 -dATdA-3 0 and 5 0 -TTT-3 0 microhelices the aromaticity of both T and dA nucleosides decrease by the DPT. This feature is in accordance to that reported in a dinucleotide (Karabıyı k, Sevinçek & Karabıyık, 2014). However, the decrease in aromaticity of dA is in contrast to its increase or almost unchanged value reported in a dinucleotide (Karabıyık, Sevinçek & Karabıyık, 2014). vi. A general noticeable increase in the non-planarity of the pyrimidine rings appears in the microhelices (Table  5) as compared to the WC with only one nucleoside pair. It is because in the helix the intermolecular Hbonds of the base pair need to be adapted to the eccentricity of the helix and its helical shape. In special, this non-planarity has large values in the torsional angles around the N1 atom. The purine rings also show a noticeable increment in its non-planarity as compared to one nucleoside pair. This non-planarity appears in general larger in the microhelices A-type (ca. 5 ) than in B-type, and it has been interpreted as result of the shift in the v angle by the torsion of the phosphate bonds (Alcolea Palafox, 2019). The DPT noticeable increments the non-planarity of the pyrimidine ring in the 5 0 -TTT-3 0 microhelix, while by contrast, it is decreased in 5 0 -dATdA-3 0 . It can be owing to several features, such as a noticeable change in the NBO negative charges on N1 and N3 atoms, and specially on O2 T,dC , O4 T and O6 dG atoms, as a result of the proton accepted or transferred, and as well the inter-plane H-bonds of the 5 0 -dATdA-3 0 microhelix ( Figure 6). The shifts in the torsional angles are ca. 3 in the pyrimidine rings, which shows their great flexibility, but as expected, it is lower in the purine rings, Table 5. The non-planarity is slightly increased in the RNA:RNA microhelices, Table  S4 (Supporting Information). vii. The exocyclic angles appear in general little affected by the DPT, Table 6. The value of the torsional angle a is related to the orientation of the phosphate group, which little change by the DPT. The torsional angle b has a large flexibility because it is related to the orientation of the O5 0 atom and it is almost unchanged by the DPT. The value of the torsional angle f has a large influence in the eccentricity of the helix. Thus, a lower value of f in the microhelices A-type than in B-type leads to an eccentricity of the helix higher in A-type than in B-type. This eccentricity is little affected by the DPT process. The endocyclic torsional angles of the furanose ring are little affected by the DPT and it does not change its symmetry. viii. The rise parameter (Dz) has lower values between purine planes than between pyrimidine planes because of larger attractive stacking interactions between purine planes. However, the value of this rise parameter is expected to remain almost constant in the helix because of the mix in each strand of purine and pyrimidine nucleosides. By contrast, if many repetitions of purine (or pyrimidine) nucleosides appear in one strand of the helix, it will lead to large difference in the rise parameter between the two strands and a deformation of the helix. The value of the rise parameter is also important because it affects the magnitude of the transferred charge between WC base pairs (Karabıyık et al., 2014). The DPT has a noticeable effect in this parameter, Figure 7, in general with a shortening of its value in the 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 microhelices A-type and a lengthening in B-type, and it has a nonignorable effect on the stacking energies as reported by Karabıyık et al. ix. The helix diameter d has in general higher values (ca. 1.2 ) and wider helix in A-type than in B-type,  Table S5 (Supporting Information), has a noticeable higher value in A-type than in B-type, 0.11 Å in 5 0 -dATdA-3 0 and 0.16 Å in 5 0 -dAdCdA-3 0 . By contrast, it is slight lower in A-type than in B-type in the 5 0 -TTT-3 0 microhelix. The DPT has a strong effect on this parameter, with a noticeable shortening of its value, especially in the 5 0 -dATdA-3 0 microhelix, ca. 0.14 Å. This shortening was also observed in the single nucleoside pair, but with lower values. xi. Mixed microhelices, such as 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 have low value of the propeller twist h p in A-type but three times higher in B-type. The effect of the DPT on h p is very small in these microhelices, about 1 , and slightly larger in 5 0 -TTT-3 0 , 3 in A-type and 7 in B-type. The value of the parameter u 0 II is almost zero in nucleobase pairs, and very small with a single nucleoside pair, but it is large in the microhelix, especially in Btype and in 5 0 -dATdA-3 0 of A-type. The DPT noticeable affects the value of this dihedral angle u 0 II ,  Table  7. The value in strand II is noticeable larger than in strand I in the 5 0 -TTT-3 0 microhelix, which indicates that the twist of the helix with the purine dA is noticeable larger than with the pyrimidine T. The values of this twist drastically change with the DPT. In the other microhelices the effect of the DPT is small, in general lower than 5 . The DPT little affects the MQR angle (Table S5 Supporting Information), which is directly related to the opening parameter (r) (Alcolea Palafox, 2019). It has high linearity in DNA:DNA helixes, in general with values close to 175 . The inclination parameter g has a low value (ca. 10 ) in the microhelices studied, and its value is little affected by the DPT, with changes around 1 to 3 .
xiii. The highest negative charge of the pyrimidine ring corresponds to the N3 and O4 atoms while in the purine ring corresponds to the N1 and N6 atoms. By DPT, the NBO negative charge of N3 in T is slightly reduced by 0.01e because it loses a proton and, by contrast, it increases ca. 0.05e in O4 when obtaining this proton, Table 7. This effect is smaller in dC, dA and dG. The DPT noticeable reduces the dipole moment m in the microhelices 5 0 -TTT-3 0 and 5 0 -dATdA-3 0 , but it has very small effect in 5 0 -dAdCdA-3 0 , Table S2 (Supporting  Information).

Summary and conclusions
The effects of the DPT on the geometrical parameters of the WC pairs with natural nucleosides and in the 5 0 -TTT-3 0 , 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 DNA:DNA microhelices of A-type and B-type were analyzed in the present manuscript for the first time. The main results obtained were the followings: 1. The DNA:DNA double microhelix structure is little destabilized by the DPT. It is slight large in 5 0 -TTT-3 0 and in 5 0 -dATdA-3 0 B-type, but small in 5 0 -dAdCdA-3 0 and 5 0 -dATdA-3 0 A-type. 2. In the helix, the non-planarity of the purine and pyrimidine rings is noticeable increased as compared to the WC with only one nucleoside pair or with nucleobases, and it was interpreted because of the intermolecular Hbonds in the base pair need to be adapted to the eccentricity of the helix and its helical shape. This nonplanarity of the nucleobase ring appears in general greater in the microhelices A-type than in B-type. The DPT noticeable increments the non-planarity of the pyrimidine ring in the 5 0 -TTT-3 0 microhelix and decreased in 5 0 -dATdA-3 0 . A slightly more flexible pyrimidine than purine rings was observed. 3. The intermolecular H-bonds ‹ and › appear in general weakened when the base pairs are in microhelices instead of in a single nucleoside pair or with nucleobases. In addition, in microhelices with mixed purine and pyrimidine in each strand, the H-bonds ‹ and › are lengthened and the DPT is again made more difficult. These features indicate that tautomerization by the DPT mechanism appears more difficult to be done in microhelices than in nucleobase or nucleoside pairs alone. 4. The DPT has a very strong effect in the intermolecular H-bonds ‹ and › with a remarkable shortening of its value and lengthening of fi. The bond angles involved in the base pair also appear affected by the DPT. The stretch parameter (Sy) has a noticeable higher value in the microhelices than in the nucleoside pairs alone or in nucleobases. The DPT has a strong effect on this parameter, with a large shortening of its value, especially in the 5 0 -dATdA-3 0 microhelix. The DPT also increases the C1 0T,dC ÁÁÁC1 0dA,dG distance between the nucleosides and opening the r angle.
5. The proton transferred from N6-H6 dA to O4 T appears weakly bonded in the dA Ã ÁT Ã base pair, and by contrast, the proton transferred from the amino group N4-H dC to O6 dG is strongly bonded in the dG Ã ÁdC Ã base pair. The DPT noticeable increases the base pairing stabilization in the dAÁT pair and by contrast decreases in the dGÁdC pair. 6. In the tautomerization process dAÁdC Ã $ dA Ã ÁdC the proton transferred H6 through the N4 dC Ã ÁÁÁH6-N6 dA intermolecular H-bond ‹ appears as the limiting step, in accordance to longer N4 dC Ã ÁÁÁH6 dA distance than N3-H dC Ã ÁÁÁN1 dA and to stronger H6-N6 dA bond than N3-H dC Ã , and to other authors. 7. The calculated CP corrected interaction energy indicates that the DPT noticeable reduces the base pairing stabilization in the dGÁT Ã mispair and by contrast it is increased in the dAÁdC Ã mispair. 8. The rise parameter (Dz) has lower values between purine planes than between pyrimidine planes. Although, its value is expected to remain almost constant in the helix with mix of purine and pyrimidine nucleosides in each strand. The DPT noticeable affects this parameter, in general with a shortening in the 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 microhelices A-type and a lengthening in B-type. 9. The helix diameter d is generally longer in A-type than in B-type. In general, the DPT shortened its value in Atype by compressing the microhelix, while the effect in B-type is opposite. The eccentricity of the helix is higher in A-type than in B-type, and the DPT slightly decreases its value in both types of helixes. 10. The propeller twist h p is low in the 5 0 -dATdA-3 0 and 5 0 -dAdCdA-3 0 mixed microhelices of A-type but three times higher in B-type. The effect of the DPT is very small in these microhelices, and noticeable high in 5 0 -TTT-3 0 .

Disclosure statement
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