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DNA is the most important biological molecule and its hydration contributes essentially to the structure and functions of the double helix. We analyze the monohydration of the individual bases of nucleic acids and their methyl derivatives using methods of Molecular Mechanics (MM) with the Poltev-Malenkov (PM), AMBER and OPLS force fields, as well as ab initio Quantum Mechanics (QM) calculations at MP2/6-31G(d,p) level of theory. A comparison is made between the calculated interaction energies and the experimental enthalpies of microhydration of bases, obtained from mass spectrometry at low temperatures. Each local water-base interaction energy minimum obtained with MM corresponds to the minimum obtained with QM. General qualitative agreement was observed in the geometrical characteristics of the local minima obtained via the two groups of methods. MM minima correspond to slightly more coplanar structures than those obtained via QM methods, and the absolute MM energy values overestimate corresponding values obtained with QM. For Adenine and Thymine the QM local minima energy values are closer to those obtained by the PM potential (average of 0.72 kcal/mol) than by the AMBER force field (1.86 kcal/mol). The differences in energy between MM and QM results are more pronounced for Guanine and Cytosine, especially for minima with the water molecule forming H-bonds with two proton-acceptor centers of the base. Such minima are the deepest ones obtained via MM methods while QM calculations result in the global minima corresponding to water molecule H-bonded to one acceptor and one donor site of the base. Calculations for trimethylated bases with a water molecule corroborate the MM results. The energy profiles were obtained with some degrees of freedom of the water molecule being frozen. This data will contribute to the improvement of the molecular mechanics force fields.

Water is one of the most abundant chemical compounds on the planet, and it constitutes a high percentage of the cell composition. To understand the role of interactions of biomolecules with water in relation to their functions, it is essential to have a detailed description of the energetic and structural aspects of interactions of the molecules involved. The first data on Deoxyribonucleic Acid (DNA) fibers obtained by X-ray diffraction showed that DNA is highly hydrated and the interactions with water are responsible for its conformational changes [

From the analysis of experimental results on hydration of oligomeric DNA duplexes, Schneider and his group [

Experimental spectroscopy studies have provided valuable data on the hydration of the components of the NA. The first studies of water clusters with nucleic bases using mass spectrometry in a primary ionization field were made by the group of Sukhodub, who determined the enthalpies of hydration of DNA bases and some of their derivatives [

The microhydration of the bases has been the subject of numerous theoretical studies by Monte Carlo [

The systems considered contain one of methylated nucleotide bases (1-methylpyrimidine or 9-methylpurine) and one water molecule. The starting geometries of the bases are the average structures obtained from X-ray experimental data in crystals, these geometries have been used in previous works [

In these equations, k is a numerical constant, q_{i}, q_{j} are the effective charges of atoms i and j respectively (calculated by semiempirical quantum chemistry methods and reproduced the experimental dipole moments of the molecules), r_{ij} is the distance between the atoms. The coefficients A_{ij}, B_{ij} and

Quantum mechanics calculations were performed using the GAUSSIAN 03W program [_{int} was evaluated considering the basis set superposition error correction using the counterpoised procedure of Boys-Bernardi implemented the GAUSSIAN package [_{BSSE} of the system is obtained.

All the local minima were verified by the calculations of the matrices of second derivatives of energy (Hessian) which appeared to be positive. For some local minima of Guanine and Cytosine more extensive basis set (aug-cc-pvdz) was used in order to confirm the geometry. For each base, energy scans were performed with both methods (MM and QM) by changing the position of the water molecule around the hydrophilic centers. Some geometric parameters were varied gradually, with other ones being fixed. For example azimuthal scans were made, i.e. the angle θ (_{x}, φ_{y} and φ_{z} which determine the rotations of the water hydrogen’s around the water oxygen were varied. The energy profiles obtained provide fine details of geometry changes which will contribute to the improvement of force fields.

The extensive calculations of the water-base systems via MM and QM methods described in the previous section enable us to reveal all the local minima for these systems. The calculated interaction energies along with those of

other authors are presented in

The structures obtained with both methods are shown in

_{W} and NH…O_{W} for the potential PM fall in the range from 1.78 to 1.98 Å while for QM they vary from 1.94 to 2.24 Å. For AMBER potentials this region extends from 1.70 to 2.12 Å, i.e. it is larger than for PM but shorter than for the quantum-mechanical calculations deviating on average by 0.16 Å from the QM values.

Comparison of the interaction energies of the minima obtained with the MM method and those obtained with QM shows generally higher values for the former, this is true for both PM and AMBER potentials (not for all the OPLS results). This difference can be due to the MM potential adjustment to the hydration of the bases in aqueous solution [_{W}…O2 distance is of 1.82 Å, while our QM calculations give the value of 1.91 Å. The same tendency took place in the Hartree-Fock study [

The values of the interaction energies in minima calculated with the method MM/PM are closer to QM ones for the Adenine and Thymine (the average differences being of 0.72 kcal/mol) than for Guanine and Cytosine (2.8 kcal/mol). The reason for these differences is due to the fact that QM calculations result in rather small interaction energies for H-bonding of water molecule to two proton acceptors of the bases. This situation will be discussed in the next section.

Minimum number | E_{PM} | E_{AMBER} | E_{OPLS} | E_{DFT} | ||
---|---|---|---|---|---|---|

9-methyladenine | ||||||

1 | −10.01 | −10.40 | −10.62 | −7.76 | −9.3^{b} | |

2 | −8.64 | −8.15 | −8.94 | −7.58 | −8.7^{b} | |

3 | −6.41 | −6.75 | −6.69 | −5.16 | ||

1-metilthymine | ||||||

1 | −4.92 | −6.96 | −8.9 | −6.40 −6.97 | −5.9^{b} −5.65^{a} | −4.6 |

2 | −8.21 | −8.74 | −9.47 | −7.48 −7.22 | −8.1^{b} −8.58^{a} | −6.8 |

3 | −7.81 | −8.05 | −10.47 | −6.46 −6.73 | −8.2^{b} −8.35^{a} | −6.5 |

4 | −5.71 | −6.71 | −9.67 | −6.28 | ||

9-methylguanine | ||||||

1 | −7.72 | −11.98 | −9.99 | −9.37 | −7.31^{c} | |

2 | −10.81 | −11.78 | −12.20 | −11.11 | −10.43^{b} −10.56^{c} | |

3 | −8.85 | −10.99 | −11.35 | −9.62 | −8.72^{c} | |

4 | −8.48 | −9.95 | −10.34 | −7.81 | −7.66^{c} | |

1-methylcytosine | ||||||

1 | −5.88 | −7.56 | −6.38 | −6.24 −6.41 | −5.24^{a} −4.5^{c} | −4.5 −4.47^{d} |

2 | −10.24 | −10.81 | −7.82 | −9.92 −9.85 | −9.97^{a} −9.1^{c} | −9.1 −8.26^{d} |

3 | −7.39 | −10.91 | −11.69 | −8.75 | −5.06^{d} | |

4 | −6.32 | −8.35 | −5.46 | −7.33 |

Structure numbering of the local minima corresponds to that of the ^{a}), RI-MP2 method from ref. [^{b}), MP2 dZ from [^{c})). E_{PM}, E_{AMBER} are the MM interaction energies calculated with PM and AMBER potentials respectively. E_{OPLS} are MM energies obtained via OPLS potentials from [_{DFT} are the interaction energy obtained with DFT method by Kim [^{d}).

The most significant differences between MM and QM results refer to the minimum 1 of Guanine and 3 of Cytosine (_{w} and O2…H_{W} resemble corresponding distances for Guanine-water complex (2.13 and 2.31 Å, respectively). With MM methods similar energy values were obtained for both force fields (

Minimum number | Hydrophilic center | PM | AMBER | MP2/6-31G |
---|---|---|---|---|

9-methyladenine | ||||

1 | N7 | 1.94 2.83 | 1.82 2.79 | 1.92 2.84 |

N6-H62 | 1.80 2.73 | 1.88 2.86 | 1.94 2.92 | |

2 | N6-H61 | 1.98 2.83 | 1.97 2.89 | 1.97 2.86 |

N1 | 1.88 2.77 | 1.83 2.79 | 2.01 2.90 | |

3 | N3 | 1.91 2.87 | 1.84 2.81 | 1.99 2.93 |

1-methyltimine | ||||

1 | O4 | 1.88 2.83 | 1.70 2.08 | 1.97 2 .91 |

2 | O4 | 1.96 2.79 | 1.76 2.69 | 1.94 2.80 |

N3-H3 | 1.86 2.75 | 2.11 3.06 | 1.93 2.83 | |

3 | O2 | 1.94 2.76 | 1.76 2.69 | 1.96 2.82 |

N3-H3 | 1.88 2.76 | 2.12 3.08 | 1.95 2.85 | |

4 | O2 | 1.87 2.83 | 1.69 2.67 | 1.95 2.90 |

9-methylguanine | ||||

1 | N7 | 1.91 2.80 | 2.01 2.94 | 2.16 3.04 |

O6 | 1.91 2.77 | 1.88 2.78 | 2.16 3.05 | |

2 | N1-H1 | 1.84 2.76 | 2.00 2.69 | 1.89 2.81 |

O6 | 1.92 2.74 | 1.79 2.72 | 1.90 2.79 | |

3 | N1-H1 | 1.91 2.76 | 2.03 2.96 | 2.43 3.25 |

N2-H21 | 1.88 2.76 | 2.07 2.97 | 1.94 2.92 | |

4 | N2-H22 | 1.86 2.78 | 1.96 2.88 | 1.94 2.83 |

N3 | 1.98 2.80 | 1.85 2.80 | 1.98 2.83 | |

1-methylcitosine | ||||

1 | N4-H42 | 1.78 2.78 | 1.88 2.89 | 2.00 2.99 |

2 | N4-H41 | 1.91 2.81 | 1.98 2.90 | 1.96 2.88 |

N3 | 1.93 2.79 | 1.86 2.79 | 1.96 2.83 | |

3 | N3 | 1.99 2.82 | 1.84 2.82 | 2.13 3.03 |

O2 | 1.96 2.68 | 2.55 3.00 | 2.31 3.02 | |

4 | O2 | 1.8 2.82 | 1.67 2.66 | 1.92 2.85 |

The first value for each center corresponds to the N-H…O_{W} or N-O_{BASE}…H_{W} distance, and the second one to N/O_{BASE}…O_{W }distance.

[

There are experimental mass spectrometry data [

The methylated bases considered in this section and compared with experimental results are: 1,4,4-trimetilci- tosine (m^{1,4,4}Cyt), 2,2,9-trimetilguanine (m^{2,2,9}Gua), and 6,6,9-trimetiladenine (M^{6,6,9}Ade). The first one excludes the minima 1 and 2 for 1-methylcytosine, the second one excludes the minima 3 and 4 for 9-methylguanine, and the last one excludes the minima 1 and 3 for 9-methyladenine (

The calculation results obtained via MM and QM methods for trimethylated bases and the experimental enthalpies of water-base complex formation are listed in the

The results demonstrate rather close experimental values of the enthalpies of complex formation with water molecule for m^{9}Gua and m^{229}Gua. The same is true for m^{1}Cyt and m^{144}Cyt (^{9}Ade and m^{669}Ade demonstrates less negative values for the trimethylated base, i.e. the substitution of amino group hydrogens by methyl groups changes the position of water molecule in the complex. Both MM and QM calculations suggest that the m^{669}Ade-water complex correspond to minimum 3 for m^{9}Ade, as the formation of other two minima for m^{9}Ade-water complexes are blocked by methyl groups.

The calculations for m^{2,2,9}Gua do not help to decide which minimum is more favorable, the minimum 1 (as predicted by PM potentials) or 2 (as predicted by QM and AMBER calculations). Both minima are possible for m^{2,2,9}Gua-water complex (^{9}Gua (

The calculations for m^{144}Cyt confirm the prediction of MM calculations (both PM and AMBER versions) on more favorable for m^{1}Cyt water position 3 (formation of two H bonds of water molecule with acceptors of the base) as compared to position 2 predicted from QM calculations. The position 2 is not possible for m^{144}Cyt-wa- ter complex, but experimental data demonstrate very close values of the enthalpy of hydration for m^{1}Cyt and m^{144}Cyt.

The calculations for trimethylated bases suggest the necessity of both improvement of MM force fields and more sophisticated QM calculations to reach more adequate description of water-base interactions.

Similar azimuthal scans were obtained for other bases; for Thymine-water system maximum energy difference,

Structure | ΔH_{EXP} [ | E_{QM} | E_{PM} | E_{AMBER} | E_{OLPS} [ |
---|---|---|---|---|---|

m^{9}Ade | −10.6 ± 1 | −10.01 (1) | −10.40 (1) | −10.62 (1) | −7.76 (1) |

m^{669}Ade | −8.3 ± 0.8 | −6.4 (3) | −7.11 (3) | −7.86 (3) | −5.16 (3) |

m^{9}Gua | −10.81 (2) | −11.98 (1) | −12.20 (2) | −11.11 (2) | |

m^{229}Gua | −14 ± 1 | −10.88 (2) | −12.21 (2) | −12.38 (2) | −11.11 (2) |

m^{1}Cyt | −11.4 ± 0.8 | −10.24 (2) | −10.91 (3) | −11.69 (3) | −9.92 (2) |

m^{144}Cyt | −11.8 ± 0.9 | −7.63 (3) | −10.91 (3) | −11.92 (3) | −8.75 (3) |

ΔH_{EXP}, the experimentally obtained enthalpies [_{QM}, the interaction energy calculated by ab initio MP2/6-31G(d,p) method. E_{PM}, E_{AMBER}, and E_{OPLS} are designated as those values in the

1.83 kcal/mol, corresponds to the trajectory from minimum 1 to minimum 2. For the Guanine-water and Cytosine-water systems, there are more pronounced differences in energy, though the distances between the participating in H bonds atoms of the base and the water molecules are rather close for the two methods. It is noteworthy that for QM structures the distances of out-of-plane water hydrogen from base acceptor atom are nearly the same as for corresponding coplanar MM water-base complexes.

The second type of scans performed refer to moving a water molecule towards and away from the base starting from the minima positions (during the optimization φ_{x}, φ_{y}, and φ_{z} parameters were varied, the angle θ was fixed). When we make a radial scan such that a water molecule approaching the methyl group of the base to the distances between the oxygen and carbon shorter than 3.15 Å, the structures obtained with MM may be non- coplanar due to the repulsion of atoms. In this case the energy dependence as a function of r for the two methods show the same pattern.

The third type of scans was performed by the displacements of water molecules out of the plane of the bases… In this case the energies have the same tendency to decrease when the water moves away from the base plane (to 90˚), at the end of the scan path there can arise a marked difference (up to 3 kcal/mol for scans near amino or methyl groups).

Some MM minima refer to both water hydrogen’s in the base plane while corresponding QM minima refer to displacement of the water hydrogen not forming H-bond by 30˚ - 45˚ out of the plane (e.g. in Thymine and Guanine 2nd minima). We performed MM and QM energy scans as functions of the angle of rotation about O-H water bond (H being H-bonded to the base and the bond being in the base plane). The energy differences between QM and MM water positions fall in 0.2 kcal/mol region, thus being not great, but may be significant for some cases. More profound QM calculations and MM parameter adjustment are required for more exact water-base system description in this respect.

This paper concerns the evaluation of the interactions of nucleic acid bases with single water molecule. The calculations for such simple systems can be performed via the methods of various complexities, from simple atom-atom MM computations of the rigid molecules to correlate ab initio QM computations using extended basis sets. The comparison of the results obtained via various methods demonstrates both some common features and some differences in quantitative geometry and energy characteristics. The simulation of biomolecular systems in surrounding water is possible via MM methods only. Thus, continuous improvement of MM force fields is required for adequate reproduction and prediction of important features of the systems containing nucleic acid fragments and hundreds of water molecules (and other biologically important molecules). Such improvement is not possible using experimental data only due to the insufficient amount of such data. The high level QM computations of the simple systems can help to fill this gap.

The comparison of the results of systematic QM MP2/6-31G(d,p) level computations with different MM methods is the first step on the pathway of MM force field refinement. Our MM computations using PM and AMBER force fields have demonstrated that each local MM energy minimum can be referred to QM one. The average energy difference between corresponding minima for Adenine and Thymine complexes with one water molecule is 0.72 and 1.86 kcal/mol for PM and AMBER force fields respectively. The differences for Guanine and Cytosine are more pronounced, especially for minima which correspond to the formation of two H bonds by water molecule with two acceptors of the bases. Such minima are global ones when calculated by MM methods while QM calculations results in global minima corresponding to the formation of one H-bonds with the base acceptor and another with base donor atom. The calculations for trimethylated bases and their comparison with experimental values of the enthalpy of monohydration supply us with evidences in favor to MM results. It became evident that additional and more extended computations via both more sophisticated QM methods and MM methods with changed force-field parameters are necessary for more exact description of base hydration. The comparison of QM and MM results for both energy minimum positions and energy dependences on selected variables should help to adjust the MM force field to the construction of detailed atom-level models of DNA fragments.

This work was partially supported by the VIEP-BUAP.

Job Lino-Pérez,Eduardo González-Jiménez,Alexandra Deriabina,Martha Velasco,Valery I. Poltev,1 1,1 1, (2016) Comparative Molecular Mechanics and Quantum Mechanics Study of Monohydration of Nucleic Acid Bases. Journal of Biophysical Chemistry,07,49-59. doi: 10.4236/jbpc.2016.72005