HAGHIGHI Ftemeh MORSALI Ali, BOZORGMEHR Mohmmd Rez BEYRAMABADI S. Ali

a (Department of Chemistry, Mashhad Branch, Islamic Azad University, Mashhad, Iran)

b (Research Center for Animal Development Applied Biology, Mashhad Branch, Islamic Azad University, Mashhad 917568, Iran)

ABSTRACT Using B3LYP and M06-2X functionals, eight noncovalent configurations for the adsorption of D-penicillamine drug (DPA) drug on poly(amidoamine) G0 generation dendrimer (PAMAMG0) carrier have been investigated. The quantum molecular descriptors and the binding and solvation energies were examined in aqueous solution and gas phase. The binding energies demonstrated the energetic stability of non-bonded species (PAMAMG0/DPA1-8). The solvation energies showed that solubility of DPA rises in the vicinity of PAMAMG0 carrier which is a fundamental factor for applicability of a carrier. Considering quantum molecular descriptors such as electrophilicity power and global hardness, the toxicity of DPA drug in the vicinity of PAMAMG0 carrier decreases and drug release is facilitated. The AIM analysis for all PAMAMG0/DPA1-8 structures indicated that the hydrogen and pseudo-hydrogen bonds play important roles in the functionalization of PAMAMG0 with DPA drug. The configuration in which DPA drug interacts simultaneously with two -NH2 functional groups of PAMAMG0 is the most stable configuration.

Keywords: DFT, D-penicillamine, hydrogen bonding, nanomedicine, poly(amidoamine) dendrimer;

1 INTRODUCTION

To reduce the side effects of anticancer drugs, a large part of the experimental and theoretical studies has recently focused on carbon-based carriers, such as dendrimers[1], drug-polymer conjugates[2], liposomes[3]C60[4,5]and carbon nanotubes[6-10]. The use of dendrimers as the host of various molecules, including drugs, and the study of the role of hydrogen bonding in these drug delivery systems have begun since 1995[10-12]. The constituent parts of dendrimers include a core located at the center of the molecule, repeated homo- centric branches bounded to the core (generations) and surface functional groups[13,14].

With appropriate properties such as surface functional groups, biocompatibility[15], tree-like structures, pseudo spherical shapes, control over the dendritic architecture[16], nano-dimensions (1～100 nm), monodispersity[17-19], their ability to cross the cell membrane[20,21]and hydrophobic cavities[22], dendrimers are convenient to carry therapeutic molecules to the target tissue[23].

Using dendrimers as the carrier molecules, lower doses of anticancer drugs are needed, resulting in reduced side effects of medicines[24-26]. Dendrimers were used as carriers for different anticancer drugs such as 5-fluorouracil[27], cis- platin[28,29], doxorubicin[30-32], famotidine[33], methotrexate[34], nifedipine[35], paclitaxel[36,37], 10-hydroxycamptothecin[38], 7-butyl-10-aminocamptothecin[39], etoposide[40], artemi- sinin[41], flutamide[42], melphalan[43], gemcitabine[44], cape- citabine[45]and 6-mercaptopurine[46]. Dendrimers were also used against HIV[47-50], Alzheimer's disease[51,52], prion diseases[53,54], inflammation[55-57]and bacteria[58-60].

Poly(amidoamine) (PAMAM) dendrimers are the most commonly used dendrimers in the drug delivery[61,62]. These carriers have been highly regarded in drug delivery due to their abilities in conjugating therapeutic molecules by host-guest interactions (formulation approach) and covalent bonding (nanoconstruct approach)[1].

Quantum computing is a powerful tool for analyzing drug delivery systems[63-71]. In this work, quantum chemical calculations were used to study the host-guest interactions of PAMAM G0 generation dendrimer with D-penicillamine drug (a sulfur-containing amino acid). D-penicillamine is used to treat various diseases, including several types of cancer[72], Wilson's disease[73,74], hepatitis[75], rheumatoid arthritis[76]and AIDS[77]. The predictions made in this way can help researchers build and use targeted anticancer drugs and reduce the process of trial and error in the laboratory.

2 COMPUTATIONAL METHOD

GAUSSIAN 09 package[78]has been utilized for the optimization of all configurations in gas and solution phases at M06-2X/6-31G(d,p) and B3LYP/6-31G(d,p). Polarized continuum model (PCM) was employed to consider the implicit solvent effects[79,80]. For the optimization of the molecular configurations, the standard convergence criteria were utilized. All degrees of freedom were optimized for all species. In addition, zero-point corrections were taken into account.

Quantum molecular descriptors may be used to evaluate chemical reactivity and stability. The global hardness (η) demonstrates the resistance of one particle against the modification in its electronic configuration.

WhereI= -EHOMOandA= -ELUMMOare the ionization potential and the electron affinity, respectively. The electrophilicity index (ω)[81]is evaluated by:

We investigated the hydrogen bond using the quantum theory of atoms in molecules (QTAIMs) calculations. QTAIM calculations are done by the AIMALL software[82]. QTAIM is based on topological parameters like electron densityρ(r)[83]. We studied various values of electron density such asGb(kinetic energy density), Vb(potential energy density), Hb(total energy density), and ▽2ρ(Laplacian of electron density) at a critical point (BCP) to distinguish the nature of the bond in different species.

3 RESULTS AND DISCUSSION

The optimized structures of poly(amidoamine) G0 generation dendrimer (PAMAMG0) and D-penicillamine

(DPA) drug have been shown in Fig. 1. The interaction of D-penicillamine including -SH, -COOH and -NH2functional groups with PAMAMG0 nanoparticles has been examined in 8 different ways (PAMAMG0/DPA1-8). The optimized structures of PAMAMG0/DPA1-4 and PAMAMG0/DPA5-8 are presented in Figs. 2 and 3, respectively (at M06-2X/6- 31G** in aqueous solution).

Fig. 1. Optimized structures of DPA and PAMAMG0

Binding (interaction) energies (ΔE) were calculated using equation (3):

Table 1 shows ΔEvalues at M06-2X and B3LYP levels in gas phase and aqueous solution. The binding energies calculated by M06-2X functional are more negative than those of B3LYP. Contrary to B3LYP, M06-2X functional considers dispersion corrections[84]. Therefore, these interactions emerge as attractive forces. ΔEsin aqueous solution (-53.1 and -30.2 kJ?mol-1on average at M06-2X and B3LYP, respectively) are more positive than those of gas phase (-60.6 and -49.2 kJ?mol-1on average at M06-2X and B3LYP, respectively), but these quantities are negative in both phases, demonstrating that the adsorption of DPA on PAMAMG0 is suitable.

ΔEdepends on the orientation of DPA relative to PAMAMG0. According to both M06-2X and B3LYP levels and both phases, among 8 configurations, PAMAMG0/DPA5 is the most stable species in which the -COOH functional group of DPA interacts with the -NH2functional groups of PAMAMG0 (Fig. 3). In terms of stability, the configurations PAMAMG0/DPA6 and PAMAMG0/DPA4 in the aqueous solution are placed in the second and third positions, respectively.

The solvation energies (ΔEsolv) have been evaluated for all optimized structures using the following equation (Table 1).

where ΔEgasand ΔEagshow the energies in the gas phase and aqueous solution, respectively.

One of the most important factors for an appropriate carrier is to increase the solubility of anticancer drugs. The solvation energy of DPA (-19.8 and -33.2 kJ?mol-1at M06-2X and B3LYP, respectively) becomes more negative in the vicinity of PAMAMG0 (-103.6 and -133.3 kJ?mol-1on average at M06-2X and B3LYP, respectively), so the solubility of DPA drug increases by PAMAMG0 carrier due to the formation of hydrogen bonds between the drug and carrier functional groups, which are further examined in detail.

Fig. 2. Optimized structures of PAMAMG0/ DPA1-4

Table 1. Binding (ΔE) and Solvation (ΔEsolv) Energies (kJ?mol-1) for Optimized Geometries

Quantum molecular descriptors (global hardness (η) and electrophilicity power (ω)) andEg(energy gap between LUMO and HOMO) for DPA, PAMAMG0 and PAMAMG0/DPA1-8 in aqueous solution and gas phase at M06-2X and B3LYP levels are reported in Table 2.

According to Table 2, Eg andηvalues of DPA and PAMAMG0 are approximately the same. These values are somewhat reduced in PAMAMG0/DPA1-8 configurations. In other words, there is no significant charge transfer between the drug and carrier. This is ideal for a drug delivery system, since the DPA drug can be easily released from the exterior surface of the PAMAMG0 carrier.Egandηvalues of PAMAMG0/DPA5 and PAMAMG0/DPA6 are more than other configurations, which indicates that they are more stable than other species. Sinceωis used to predict toxicity, it can be concluded that the toxicity of DPA drug is reduced in the vicinity of the PAMAMG0 carrier. Theωvalues of DPA are higher than those of PAMAMG0/DPA1-8 in both phases, which demonstrates that DPA plays the role of electron acceptor.

Fig. 3. Optimized structures of PAMAMG0/ DPA5-8

Table 2. Quantum Molecular Descriptors (eV) for Optimized Geometries

Charge density properties were used to examine the intermolecular hydrogen bonds more accurately. These interactions were studied by QTAIM analysis. The strength and characteristic of an interaction can be demonstrated byρ(r) and ?2ρ(r), respectively. On the other hand, the nature of the interactions may be represented by the signs of ?2ρandHb. If (?2ρ＞ 0,Hb＞ 0), (?2ρ＞ 0,Hb＜ 0) and (?2ρ＜ 0,Hb＜ 0), weak, medium and strong interactions are expected, respectively[85]. The character of an interaction can be explained by -Gb/Vb. For -Gb/Vb＞ 1 and 0.5 ＜-Gb/Vb＜1, noncovalent and partially covalent characters are expected, respectively.

Table 3. Topological Parameters in a.u. and the Hydrogen Bond Energy (EHB) in kJ?mol-1 for PAMAMG0/DPA1-8 at M06-2X in Aqueous Solution

The molecular graphs of PAMAMG0/DPA1-4 and PAMAMG0/DPA5-8 in aqueous solution at M06- 2X/6-31G** are shown in Figs. 4 and 5, respectively. In these figures, the atoms involved in the interaction of drug with the carrier marked. The values ofρ(r), ?2ρ(r),Hb,Gb,Vband -Gb/Vbfor these interactions at M06-2X level in aqueous solution are presented in Table 3. We evaluated the hydrogen bond energies (EHBby the following equation[86]).

In PAMAMG0/DPA1-8 configurations, we encounter three important types of hydrogen and pseudo-hydrogen bonds,i.e., O-H, N-H and S-H. We begin the investigation with the most stable configuration (PAMAMG0/DPA5), in which the -COOH functional group of DPA approaches two -NH2functional groups of PAMAMG0 simultaneously. The H(95)?? N(35) (EHB= -102.0 kJ?mol-1), H(97)?? N(17) (EHB= -21.37 kJ?mol-1) and H(18)? O(91) (EHB= -17.6 kJ?mol-1) interactions with ?2ρ＞ 0,Hb＜ 0, 0.5＜-Gb/Vb＜1 are medium hydrogen bonds, the first of which H(95)? N(35) with -Gb/Vb= 0.6236 is close to strong hydrogen bonds. The H(77)?? O(91), H(78)?? N(89) and H(101)?? N(17) interac- tions (EHB(avarge) = -7.6 kJ?mol-1) with ?2ρ＞ 0,Hb＞ 0 and -Gb/Vb＞ 1 belong to weak hydrogen bonds.

Fig. 4. Molecular graph of PAMAMG0/ DPA1-4. Small green spheres and lines related to the bond critical points (BCP) and the bond paths, respectively

In PAMAMG0/DPA6, as the second most stable structure, -OH from -COOH functional group of DPA approaches -NH2functional groups of PAMAMG0. This configuration has 1 medium hydrogen bond withEHB= -93.1 kJ?mol-1and -Gb/Vb= 0.6518, the properties of which are similar to strong hydrogen bonds. Two other interactions (H(80)? O(91) and H(78)?? O(91)) are classified as weak hydrogen bonds.

The third most stable structure is PAMAMG0/DPA4, in which -COOH functional group of DPA interacts with -NH2and -C=O functional groups of PAMAMG0, simultaneously. The H(3)?? O(91) (EHB= -20.9 kJ?mol-1) and H(95)? O(8) (EHB= -72.8 kJ?mol-1) interactions with ?2ρ＞ 0,Hb＜ 0 and 0.5 ＜ -Gb/Vbare medium hydrogen bonds and three other interactions are week. Two of these weak interactions are related to S-H interactions (H(83)? S(90)and H(81)? S(90)). The structure of PAMAMG0/DPA2 is very similar to PAMAMG0/DPA4, except that there are no H???S interactions.

PAMAMG0/DPA1 has 1 medium hydrogen bond (H(97)? O(8) withEHB= -24.1 kJ?mol-1and four weak interactions, in which -NH2functional group of DPA approaches -C=O functional group of PAMAMG0. PAMAMG0/DPA7 and PAMAMG0/DPA8 have approxima- tely the same stability. In the former, -COOH and -NH2functional groups of DPA interact with the -NH functional groups of PAMAMG0, and in the latter the -NH2functional group of DPA interacts with the -NH2functional group of PAMAMG0. PAMAMG0/DPA7 has six weak hydrogen bonds, one of which is close to a medium interaction (H(22)? O(91) withEHB= -20.7 kJ?mol-1). On the other hand, PAMAMG0/DPA8 has one medium hydrogen bond (H(96)? N(17) withEHB= -22.0 kJ?mol-1) and one weak interaction. The most unstable configuration is related to PAMAMG0/DPA3, in which the -SH functional group of DPA approaches the -NH functional group of PAMAMG0. This structure has 3 weak interactions withEHB(avarage) = -6.0 kJ?mol-1, two of which are related to S-H interactions (H(22)? S(90)and H(76)?? S(90)).

Fig. 5. Same as Fig. 4 for PAMAMG0/ DPA5-8

4 CONCLUSION

Eight configurations of noncovalent adsorption of D-penicillamine (DPA) drug on poly(amidoamine) G0 generation dendrimer (PAMAMG0) were examined at B3LYP and M06-2X density functional levels in aqueous solution and gas phase (PAMAMG0/DPA1-8). The simulta- neous interaction of two -NH2functional groups of PAMAMG0 with -COOH functional group of DPA leads to the most stable configuration (PAMAMG0/DPA5).

The values of solvation and binding energies show that the functionalization of PAMAMG0 with D-penicillamine drug is energetically suitable. Solvation energies indicated that the solubility of DPA drug increases in the presence of PAMAMG0. Considering the HOMO-LUMO energy gap, electrophilicity power and the global hardness, the toxicity of DPA in the vicinity of PAMAMG0 decreases. Also, according to the AIM studies, DPA can be noncovalently functionalized on PAMAMG0/DPA through hydrogen and pseudo-hydrogen bonds. The AIM results indicated that stronger and more hydrogen bonds exist in the most stable configuration (PAMAMG0/DPA5). The most unstable structure (PAMAMG0/DPA3) occurs when the -NH functional group of PAMAMG0 interacts with the -SH functional group of DPA.