**3.6. Profiles of the physico-chemical parameters along the IRC of tautomerizations**  *via* **DPT and PT**

We developed original methodology tracking the evolution of all physico-chemical parameters along the entire reaction pathways: in particular, the electronic energy, the first derivative of the electronic energy by the IRC-dE/dIRC, the dipole moment of the base pair, the distances and the angle of the intermolecular specific contacts (H-bonds or van der Waals contacts), electron density, the Laplacian of the electron density, ellipticity and the energy at the (3,-1) bond critical points of the intrapair specific contacts, the NBO charges of the hydrogen atoms involved in the tautomerization, the glycosidic angles and the distance between the glycosidic hydrogens. This works not only in the stationary structures such as reagent, product and transition state of the tautomerizations *via* the DPT and w↔WC tautomeric reactions *via* the PT [51–74, 78].

Additionally, for the first time, we have introduced the conception of the key points (KPs) based on the electron-topological characteristics of the intermolecular bonds, namely the value of the electron density and its Laplacian at the corresponding (3,-1) bond critical points. This approach allows us to comprehensively describe the mechanism of the tautomerization process. Thus, depending on the symmetry and nature of the system, maximum number of KPs could reach 9 and minimal—5, when KPs are degenerated (see **Figures 5** and **6** for illustration on the example of the 2AP·T(WC)↔2AP·T\*(w)).

tautomerizing into the pair with Watson-Crick architecture of the binding. For the case, when A belongs to the template strand of DNA: A + C → A·C → A·C\*, A +A → A·A → A\*·A → A\*·Asyn,

**Figure 4.** Structures corresponding to the stationary points on the reaction pathways of the (a) A\*·A(WC)↔A\*·Asyn(TF), (b) G·A(WC)↔G·Asyn, (c) A\*·G\*(WC)↔A\*·G\*syn and (d) G·G\*(WC)↔G·G\*syn *anti*↔*syn* conversions through the large-scale adjustments of the bases relative to each other, obtained at the B3LYP/6–311++G(d,p) level of theory, ε = 1 [77].

Both processes have two common features—they involve the same pairs, which play the role of intermediates on the path of formation of enzymatically competent conformations of some incorrect pairs, as well as the same set of terminal incorrect pairs, able to acquire the enzy-

matically competent conformations during the process of thermal fluctuations.

A + G → A·G → A\*·G\* → A\*·G\*syn.

40 Mitochondrial DNA - New Insights

Arrangement of the extrema of the derivative of the energy by IRC—dE/dIRC—coincides with the second and penultimate KPs, where mutual transformations of the H-bond into a covalent bond and *vice versa* occur. These data allow us to separate the pathway of the tautomerization reaction into the zones of reagent, transition state and product of the reaction. In general, these key points could be considered as "fingerprints" of the tautomerization process *via* DPT or PT.

**Figure 5.** Geometric structures of the nine key points with their IRC coordinated describing the evolution of the 2AP·T(WC)↔2AP·T\*(w) tautomerization *via* the single PT and sequential shifting of the bases relative to each other within the base pair into the minor groove side of the DNA helix along the IRC obtained at the B3LYP/6–311++G(d,p) level of theory, ε = 1 [79] tautomerization). At this point, three KPs correspond to the two abovementioned local minima (the first and the last KPs–reagent and product, respectively) and transition state of the tautomerization. Other KPs include two KPs, for which migrating proton is localized midway between the electronegative atoms involved in the specific contact and are characterized by the loosened A-H-B covalent bridge, and also four key points, in which the H-bonds begin to acquire the features of the covalent bond and *vice versa*, that is where the Laplacian of the electron density passes through zero: Δρ = 0.

**Figure 6.** Profiles of: **(a)** the relative electronic energy ΔE, **(b)** the first derivative of the electronic energy with respect to the IRC (dE/dIRC), **(c)** the dipole moment μ, **(d)** the electron density ρ, (**e**) the Laplacian of the electron density Δρ, (**f**) the energy of the intermolecular H-bonds EHB estimated by the EML formula [79] at the (3,-1) BCPs, (**g**) the distance dA···B between the electronegative A and B atoms, (**h**) the distance dAH/HB between the hydrogen and electronegative A or B atoms and (**i**) the angle ∠AH···B of the covalent and hydrogen bonds along the IRC of the 2AP·T(WC)↔2AP·T\*(w)

Renaissance of the Tautomeric Hypothesis of the Spontaneous Point Mutations in DNA: New Ideas…

http://dx.doi.org/10.5772/intechopen.77366

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**Figure 7.** Geometrical structures of the 12 incorrect DNA base mispairs causing spontaneous point incorporation and

tautomerization obtained at the B3LYP/6–311++G(d,p) level of theory, ε = 1.

replication errors (B3LYP/6–311++G(d,p) level of theory, ε = 1).

This methodology enables to make an objective conclusion about the character of tautomerization (concerted, synchronous or asynchronous), quantitatively estimate the cooperativity of the specific intermolecular interactions (namely, H-bonds, in particular nonclassical CH···O/N or dihydrogen AH···HB H-bonds, loosened A-H-B covalent bridges and attractive A···B van der Waals contacts), sequentially changing each other along the IRC of the tautomerization, and trace how these interactions are grouped into the patterns (from 9 to 15) and how they successively substitute each other along the IRC of tautomerization.
