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^{2}Islamshahr Branch, Islamic Azad University Tehran, Iran

^{3}Tehran Shargh Branch (ghyamdasht), Islamic Azad University,
Tehran, Iran

^{*} To whom correspondence should be addressed.

Received January 9, 2005; Revision received April 18, 2005

The combination of Quantum Mechanics (QM) and Molecular Mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM/MM method has been used for different types of problems, for example: structural biology, surface phenomena, and liquid phase. In this paper, we have used these methods for antibiotics and then we compare results. The calculations were done by the fullab initiomethod (HF/3-21G) and the (HF/STO-3G) and QM/MM (ONIOM) method with HF (3-21G)/AM1/UFF and HF (STO-3G)/AM1/UFF. We found the geometry that has obtained by the QM/MM method to be very accurate, and we can use this rapid method in place of time consumingab initiomethods for large molecules. Comparison of energy values in the QM/MM and QM methods is given. In the present work, we compare chemical shifts and conclude that the QM/MM method is a perturbed full QM method. The work has been done on penicillin, streptomycin, benzyl penicillin, neomycin, kanamycin, gentamicin, and amoxicillin.

KEY WORDS: quantum mechanics, molecular mechanics,ab initiocalculations, antibiotics

DOI: 10.1134/S0006297906130190

Various computational approaches have strengths and weaknesses. Dramatic progress has been made in the field of computational chemistry in recent years. Molecular mechanics can model very large compounds rapidly. Quantum mechanics is able to compute many properties and model chemical reactions. Of course, QM/MM approaches are different and depend on the methods used for calculations in the QM and MM regions. However there are many other attributes characterizing the various published methods. Chemical systems of interest in computational biology and reaction catalysis are occasionally systems in condensed phase that consist of thousands of participating atoms.

The combination of quantum and molecular mechanics gives very rapid results where only one part of the molecule needs to be modeled quantum mechanically. Today, it is well accepted that the QM method is the ultimate computational tool that can be used successfully in studying the structural aspects of a molecule and a variety of its physical and chemical properties.

Using these calculations energy, bond lengths, bond angles, the strongest bonds, estimation of the active site of a molecule, recognition of reaction mechanism in the body, type of penetration in living cells, and also the presence of antibiotic drug residues in food products of animal origin that has potential health hazard to consumers can be obtained. For example, sulfonamide residues in some species have been a problem for about 10-12 years. Such studies are widespread for biological systems, especially enzymes [1-8].

In this study, the QM/MM method is focused on antibiotics [4]. The geometries and NMR shielding tensors have been calculated. The calculated values from both methods (QM and QM/MM) were compared and the results were very close together except in time consumption. For example, optimization times for the largest molecules in this study--kanamycin, streptomycin, and gentamicin--are given in Table 1.

**Table 1.** Comparison of time consumption for
the three largest antibiotics

**METHODS OF INVESTIGATION**

** Computational details.** The GAUSSIAN 98 software package [9] is used to perform Hartree-Fock (HF) and DFT
calculations, B3LYP and LSDA, on the antibiotics. The semiempirical
calculation is based on the AM1 method and because we use the Gaussian
98 program we must take UFF force field for the molecular mechanic
part. Hybrid QM/MM runs were performed as implemented before in the
ONIOM method. In many respects, the issues governing implementation of
QM/MM computer codes are similar to those associated with the
individual QM and MM methods. Most of the coupling terms are readily
computed using the machinery present in either the QM or MM packages.
However, it is worthwhile to give brief consideration to a couple of
implementation issues. Given that the starting point is working QM and
MM codes, QM/MM implementations can be considered to fall into three
groups [10].

I. Those based on classical modeling packages with a QM code integrated as a force field extension 3.

II. Those based on a QM package incorporating the MM environment as a perturbation.

III. Modular schemes in which a central control program is provided and a choice of both QM and MM methods is left open.

** Methodology. **On the basis of the ONIOM method, we divided every
molecule into three parts (L, M, and H) and then optimized each
point. This method cannot optimize some molecules because of having a
double bond or aromatic ring in the link part. The link bonds are a
critical aspect of the QM/MM method. Usually, we use a dummy atom to
complete the QM subsystem. We must note that the link part should
always be in the form of
C_{alpha}-C_{beta} for two subsystems
QM/MM. In fact, the relation between the link part and MM or QM
subsystems must be through one atom. The QM/MM boundary should not cut
across double, triple, or aromatic bonds as [11].
Thus, one link atom can only be bonded to one QM atom. But the reverse
situation is allowed; this means that two link atoms are bonded with
one QM atom.

The separation of the partial atomic driving force is described as
follows. In the ONIOM calculation of the total energy,
*E*^{REAL}_{ONIOM }(R_{1}...
R_{N}; r_{m+1},r_{m+2}) is approximated by:

*E*^{REAL}_{ONIOM }(R_{1}...
R_{N}; r_{m+1},r_{m+2}) =
**E**^{REAL}_{MM
}(R_{1}...R_{N}) + **E
**^{MODEL}_{QM }(r_{1}...r_{m},
r_{m+1},r_{m+2}) - **E
**^{MODEL}_{MM }(r_{1}...r_{m},
r_{m+1},r_{m+2}),

where the REAL system consists of N atoms at R_{i }(i = 1,
2...N) and the MODEL system consists of (m+2) atoms at r_{j
}(j = 1, 2...m+1, m+2) [12].

**RESULTS AND DISCUSSION**

According to [12],
**E**^{REAL}_{ONIOM }(R_{1}...
R_{N}; r_{m+1},r_{m+2}) is the total ONIOM
optimized energy for each antibiotic, R_{1}...R_{N }are
the coordinates for each atom (1...N) of the molecules, and
r_{m+1},r_{m+2 }are the coordinates for link atoms.
**E**^{REAL}_{MM
}(R_{1}...R_{N}) is the total MM optimized energy
for R_{1 }to R_{N}.
**E**^{MODEL}_{QM
}(r_{1}...r_{m}, r_{m+1},r_{m+2})
is the total QM optimized energy for the medium region and link atoms
and **E**^{MODEL}_{MM
}(r_{1}...r_{m}, r_{m+1},r_{m+2})
is the total MM optimized energy for the medium region and link atoms
[10].

In the present work, we compare the result from pure quantum mechanical
(*ab initio*) calculation of a molecule and the QM/MM results. The
calculations were performed using the GAUSSIAN 98 software package [9]. We conclude that these two data groups are in good
agreement. Then we can use the QM/MM method for recognizing the active
site of antibiotic molecules and mechanism of their reactions in the
body. In all test examples the results of QM/MM calculations were
compared to the corresponding results of full quantum chemical study.
The optimized geometries are summarized in Table 2.

**Table 2. **Geometric data
comparison^{a}

^{a}Bond length in Angstroms and angles in degrees.

^{b}H, M, and L are related to the level of calculation.

^{c}After optimization, the atom number is different in each method, so we wrote the equal positions. The upper is the nomenclature in QM and the lower in QM/MM.

In *ab initio *quantum chemistry, analytical derivative theories
have made possible the calculations of many important molecular
properties. It should be pointed out that a direct comparison of the
QM/MM predictions to the experimental data available for the same
molecular system is complicated by the fact that the empirical
parameterization contained in the MM force fields is partly responsible
either for excellent agreement (may be due to successful cancellation
of errors) or serious disagreement between two sets of values. In the
ONIOM method that we use in this work, particle exchanges between
high-level and 4 low-level subsystems do not disturb the statistical
ensemble. NMR shielding tensors (ppm) have been computed with the
continuous set of the gauge independent atomic orbital (GIAO) method
[13-16]. The
*delta*_values for isotropy and anisotropy are shown in Figs. 1-4.

Fig. 1.Calculated NMR isotropy by QM and QM/MM methods for amoxicillin (1), neomycin (2), and gentamicin (3).

Fig. 2.Calculated NMR isotropy by QM and QM/MM methods for penicillin N (1), streptomycin (2), benzyl-penicillin (3), and kanamycin (4).

Fig. 3.Calculated NMR anisotropy by QM and QM/MM methods for amoxicillin (1), neomycin (2), and gentamicin (3).

As we see in NMR isotropy and anisotropy for all of the molecules (Table 3), in the high region of calculations a similar trend is obtained for the QM and QM/MM methods [17-19]. In the medium and low regions (semiempirical and molecular mechanic parts) some perturbations were observed in the form of the following equations:

Fig. 4.Calculated NMR anisotropy by QM and QM/MM methods for penicillin N (1), streptomycin (2), benzyl-penicillin (3), and kanamycin (4).

where

where * s *is the number of atoms in the MM part and

where * q_{s }*is atomic charge on MM atom,

*E _{Total }= *

**Table 3. **Comparison between resulting QM and
QM/MM isotropy, anisotropy, and chemical shift anisotropy asymmetry
(Etha)

In this part of the calculations two dummy atoms (H) are entered in the
molecule and the chemical environment of atoms differ with the primary
structure. In the full *ab initio *method, the hydrogen and carbon
atoms have similar chemical environment and their chemical shifts are
approximately uniform. Therefore, simply we can see the effect of
isolation of parts in NMR spectra. Usually the heavy atoms that contain
electron pairs have high *delta*_values and display peaks.

The energy values for some different *ab initio *and DFT methods
and the comparison between the QM and QM/MM methods are given in Table
4. As observed geometrical values are very close
in the two methods and where the *ab initio *calculations are not
possible, for example, in molecules consisting of 100 or greater number
of atoms, we can use QM/MM results with complete assurance.

**Table 4. **Optimized structure of different
antibiotics with their energies (Hartree) by QM and QM/MM methods

This brief review of the QM/MM approach has emphasized the variety of ways that QM and MM calculations can be combined. As may be clear from the number of variations that are possible it will probably be difficult to get exactly the same answer 5 with two separate implementations and like the force fields themselves the methodology will gradually gain acceptance on the basis of experience.

The QM/MM model for describing biomolecules, while successful, still requires further development which will lead to a better integration of the QM and MM formalisms by solving the problem of the QM/MM boundary in a general way. Thus it is expected that both the development and the application of QM/MM method will continue to expand strongly in the current decade and that the information obtained from QM/MM calculations will be essential for a deep understanding of biochemical processes. A number of other systems are currently under study with the new QM/MM methods that have been developed recently in this group. Implementations of the algorithm to calculate NMR chemical shielding tensors in the QM/MM framework makes it possible to study the chemical shift of specific group in biomolecules.

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