*3.1.3. Analysis of the electron and geometric structures of hydrogen bonds in complementary pairs within the NA double helix by the PM3 method*

Let us construct a model NA double helix of six nucleotide pairs (C-G, А-Т, Т-А, G-C, C-G, and А-Т) and fully optimize their electron structure by the PM3 method.

The results showed that a right-turn helix is produced (Fig. 6), which agrees with experimental data. The lengths of the hydrogen bonds in the DNA double helix coincide within 0.02 Å with those computed for isolated nucleotides. The energy of the hydrogen bonds is Е = -8.82 kcal/mol per nucleotide pair, which is approximately the average of the energies in two different nucleotide pairs (-5.55 and -11.73 kcal/mol). Thus, the results of computations make it possible to assume that only the above interactions in nucleotide pairs occur in DNA and that there are no other significant interactions.

272 The Complex World of Polysaccharides

nucleotides (Table 5).

the atoms involved in hydrogen bonding.

above, these results suggest quite stable hydrogen bonds.

(Mulliken R.S.,1955) showed that the charge of the hydrogen atoms is positive, about +0.5е, while the interacting O and N atoms have a negative charge ranging from –0.68 to –0.83е. As

Then, we performed *ab initio* calculations for noncomplementary pairs of adenine with other

Т-А C-G

**Figure 5.** Hydrogen bonding in the complementary pairs АТ and CG. Quantum chemical computation by the *аb initio* method in the 6-31G\* basis. The charges computed according to Mulliken are shown for

Е = -11.78 kcal/mol Е = -25.39 kcal/mol

Nucleotides **Т А C G** 

As Table 5 demonstrates, selection of complementary T for A is not most advantageous in terms of energy. The interactions AC and AG are more advantageous. The selectivity of nucleotide matching is due to the specific geometric structure of the NA double helix (Fig. 4) (Singer M., Berg P. 1998). Thus, *ab initio* calculations in the 6-31G\* basis confirmed that complementarity in the AT and CG pairs is determined mostly by the orientation of hydrogen bonds formed between the interacting nucleotides and the distance between deoxyribose

Let us construct a model NA double helix of six nucleotide pairs (C-G, А-Т, Т-А, G-C, C-G,

The results showed that a right-turn helix is produced (Fig. 6), which agrees with experimental data. The lengths of the hydrogen bonds in the DNA double helix coincide within 0.02 Å with those computed for isolated nucleotides. The energy of the hydrogen bonds is Е = -8.82 kcal/mol per nucleotide pair, which is approximately the average of the energies in two different nucleotide pairs (-5.55 and -11.73 kcal/mol). Thus, the results of

residues in the NA double helix, rather than by the energy of hydrogen bonding.

*3.1.3. Analysis of the electron and geometric structures of hydrogen bonds in* 

*complementary pairs within the NA double helix by the PM3 method* 

and А-Т) and fully optimize their electron structure by the PM3 method.

Note: Energy (kcal/mol) was estimated by *аb initio* calculations in the 6-31G\* basis. **Table 5.** Energy of hydrogen bonds in pairs of A with T, A, C, and G

**А -11.78 -8.93 -12.51 -13.84** 

Е = -8.82 kcal/mol per nucleotide pair

**Figure 6.** Hydrogen bonding in complementary pairs AT and CG contained in the DNA double helix (exemplified by a 6-bp duplex). Quantum chemical computation by the PM3 method.

Computations performed for mismatching nucleotide pairs contained in the NA double helix yielded the following picture. In the case of two pyrimidines (T and C), the energy of interaction is equal to zero, because the internucleotide distance is too high. In the case of two purines (A and G), there is not sufficient room for the nucleotides: their rings are bent and the sugar-phosphate backbones forced apart. This is disadvantageous in terms of energy; the loss in electron energy is about 120 kcal/mol. The interactions of T with G and A with C are also disadvantageous, because the parallel arrangement of nucleotides is distorted.

Thus, the quantum chemical computations allow the following conclusions.


At the next step, we studied the possibility of complexation of NA bases with carboxyl or hydroxymethyl groups of polysaccharides. The questions were whether hydrogen bonds can be formed between NA bases and sugars and how the four NA bases interact with polysaccharide structural units (UDP-glucose and UDP-glucuronic acid). In addition, it was important to analyze how selectivity may be achieved in template synthesis of a polysaccharide (e.g., HA) on NA.

*3.1.4. Quantum chemical analysis of the electron and geometric structures of hydrogen bonds in complementary pairs of NA and polysaccharides by the PM3 method* 

First, a model was selected for calculations. We found that substitution of glucuronic acid for UDP-glucuronic acid does not affect the hydrogen bonding parameters, but substantially reduces the computation time. Hence the UDP moiety attached to a sugar was omitted in further computations.

Let us assume that NA interacts with the carboxyl or hydroxymethyl group linked to C5 of a monosaccharide unit. Complete optimization of the geometric structure was performed for complexes formed with various initial arrangements of NA bases and glucuronic acid, and several local minima of potential energy were revealed. Among the resulting structures, those with the highest energy of interactions between the components were selected for each NA base–glucuronic acid pair (Fig. 7).

**Figure 7.** Formation of hydrogen bonds between the carboxyl group of glucuronic acid and DNA bases. Quantum chemical computations by the PM3 method.

The complex structure shows clearly that two hydrogen bonds are formed and are nearly in the same plane, as in the case of the T–A interaction. The most important in this situation is that the bonds have approximately the same lengths and binding energies as in the complementary pairs AT and GC. In addition, Fig. 7 shows that the interactions of the carboxyl group with the nucleotides are nonequivalent. The interactions with G and A are more efficient than with T and C, which is determined by the geometry of the hydrogen bonds. A hydrogen bond should be of a certain length and orientation relative to other atoms, and the conditions for hydrogen bonding are better in some cases and poorer in some others.

274 The Complex World of Polysaccharides

further computations.

polysaccharide (e.g., HA) on NA.

NA base–glucuronic acid pair (Fig. 7).

Quantum chemical computations by the PM3 method.

important to analyze how selectivity may be achieved in template synthesis of a

First, a model was selected for calculations. We found that substitution of glucuronic acid for UDP-glucuronic acid does not affect the hydrogen bonding parameters, but substantially reduces the computation time. Hence the UDP moiety attached to a sugar was omitted in

Let us assume that NA interacts with the carboxyl or hydroxymethyl group linked to C5 of a monosaccharide unit. Complete optimization of the geometric structure was performed for complexes formed with various initial arrangements of NA bases and glucuronic acid, and several local minima of potential energy were revealed. Among the resulting structures, those with the highest energy of interactions between the components were selected for each

**Figure 7.** Formation of hydrogen bonds between the carboxyl group of glucuronic acid and DNA bases.

C - glucuronic acid Т - glucuronic acid

 ∆Е= - 7.79 kcal/mol ∆Е= - 6.39 kcal/mol

The complex structure shows clearly that two hydrogen bonds are formed and are nearly in the same plane, as in the case of the T–A interaction. The most important in this situation is that the bonds have approximately the same lengths and binding energies as in the

*3.1.4. Quantum chemical analysis of the electron and geometric structures of hydrogen* 

*bonds in complementary pairs of NA and polysaccharides by the PM3 method* 

G - glucuronic acid А - glucuronic acid

∆Е= -8.54 kcal/mol ∆Е= -7.91 kcal/mol

Then, the PM3 method was used to study the possibility of interactions between the bases and the hydroxymethyl group of N-acetylglucosamine. Several initial arrangements of a base and N-acetylglucosamine were analyzed for each of the four bases. Optimization of the initial arrangement allowed several modes of binding. Among the resulting structures, those with the highest energy of interactions were selected. The results are shown in Fig. 8.

**Figure 8.** Formation of hydrogen bonds between the hydroxymethyl group of N- acetylglucosamine and the DNA bases. Quantum chemical computations by the PM3 method.

Let us consider the specifics of hydrogen bonding between the nucleotides and the hydoxymethyl group of N-acetylglucosamine. It is known that hydrogen bonds formed by the hydroxymethyl group are less stable than those formed by the carboxyl group (Roberts J., et al. 1978). As complete optimization of the geometric structures showed, the energy of hydrogen bonds was indeed higher in the complexes of the NA bases with the hydroxymethyl group of N-acetylglucosamine (Fig. 8) than in the complexes with the carboxymethyl group (Fig. 7). Optimization of the geometric structure for complexes of the

bases with N-acetylglucosamine with various initial arrangements of the interacting groups yielded complexes with one or two hydrogen bonds. Complexes containing one hydrogen bond were most advantageous in terms of energy according to PM3 computations. The nucleotides proved to vary in energy of interaction with the hydroxymethyl group: the interaction was more efficient with T and C than with G and A. The conclusions are as follows.

