INTRODUCTION

Bone tissue tolerates constant rebuilding and achieves the equilibrium by osteoblasts producing bone and osteoclasts destroying bone. The compounds of bisphosphonates keep from the digestion of bone by pushing osteoclasts to bear cell death or the apoptosis, which diminish the velocity of bone destroying ^[1].

The principal impact of the active bisphosphonates is to prevent bone resorption. In fact, these structures manifest to be strong inhibitors of resorption when experimented in various conditions of in vivo and in vitro. Bisphosphonate compounds stop bone resorption produced by different reasons in cell and organ. They prevent forming the holes by isolated osteoclasts on mineral layers ^[2].

Generally, the physicochemical impacts of bisphosphonates are very close to those of pyrophosphate. Therefore, they prevent the formation, postpone the association, and decrease the dissolution of calcium phosphate compounds. All these impacts depend on the identified intention of these structures for solid-phase calcium phosphate, on the surface of which they attach extremely. This notable characteristic is the basis for the employment of these structures as skeletal markers in nuclear medicine and the foundation for their selective localization in bone when employed as the drugs. There is an attention to enhancing the bioavailability and duration of action of a drug to modify therapeutic consequences. Drug delivery technique is able to change a drug's pharmacokinetics and specificity by formulating it with various ingredients, drug carriers, and medical equipment ^[3]-^[7].

Nanomedicine covers a wide range of therapeutic applications, from nanoparticulate drug delivery systems including carbon nanotubes, layered double hydroxides, to in vitro (biosensor) and in vivo (imaging and implantable devices) diagnostics ^[8]-^[13]. Nanomedicine in drug delivery is for achieving the improved delivery of water insoluble drugs, delivery of large macromolecule drugs to intracellular sites of action, and codelivery of two or more drugs or therapeutic agents for combination remedy ^[14]-^[16]. Since the exploring CNTs in 1990s and the progress of their application in nanomedicine, these compounds are significant through their properties including rich electronic and thermal factors, great mechanical strength, high chemical stability, and extremely lightweight ^[17]-^[19]. These carriers indicate the capability for transferring the therapeutic agents such as proteins, DNA, antibodies and drugs on the external wall or by trapping in the cavity nanotubes as a capsule ^[20]-^[22].

Nanotubes with their intrinsic properties have been considered potential candidates for drug delivery carriers. The capped ends of nanotubes may be opened up by oxidation, allowing for the insertion of molecules of interest inside the nanotube. Carbon nanotubes (CNTs) can easily penetrate cells, delivering drugs directly to the cytoplasm or nucleus.

CNTs are large molecules that are built by repeating pattern of sp2 hybridized carbon atoms in a hexagonal composition, rolled into a cylinder of approximately 2.5-100 nm in diameter. CNTs are long and tubular fullerene structures, which can be either single-walled (SWCNTs) or multiwalled (MWCNTs). SWCNTs are formed by a rolling single layer of graphite cylinder with a tube diameter of approximately 0.4-2 nm, but MWCNTs are multiple concentric cylindrical shells of graphite layers with the distance about 0.36 nm and diameters about 2-100 nm. Nanotubes conform to a perpendicular position with the cell membrane during uptake, perforating and diffusing through the lipid bilayer to enter the cytoplasm. Functionalized CNTs are easily internalized by cells through passive and endocytosis-independent mechanisms ^[1]-^[6].

The bone cells in human body are gradually being continually taken away and substituted with new ones by osteoblast in the total life. The bisphosphonates behave by reducing osteoclast activity and then reducing the overturn of bone or replacement of the old bone cell. Since we start being old and in particular, a disease, the bone is really being damaged or removed more quick than our body can substitute it. This makes the bones weakened, thin and much easily to break with even a small impact or a fall from a standing height. Therefore, bisphosphonate medications support us to keep the bone density and bone strength.

In fact, the most popular bisphosphonate medications have a rich tension for metal cations, among them Ca²⁺, with which they can produce both soluble and insoluble compounds and aggregates, depending on the pH of the solution and the metal exist. The bisphosphonates are separated into chemical branches based on the side chains of R1 and R2. It is seen a central carbon in bisphosphonates with two side chains of R1, R2 and two phosphate branches which are bonded to Ca²⁺ through O- of PO₃ groups for keeping a high amount of Ca²⁺ in bones of human body cells ^[23]-^[29] (Scheme 1).

In this article, we have focused more on recent bisphosphonate drugs such as 5AEL, 5AFX,4QPF, 3DYG, 2F92, 2I19 which have been chelated with Mg²⁺, Ca²⁺, Sr²⁺ adsorbed onto (5,5) armchair SWCNT, respectively (Scheme 1). This new generation of bisphosphonates agents of 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 as second and third generation of bisphosphonates consist of nitrogen atoms in side chain of R2 for promoting osteoclast apoptosis (Scheme 1). Therefore, sicks obtain the cure with more intense nitrogen bisphosphonates rather than the earlier non nitrogen bisphosphonates.

Scheme 1 Proposed mechanism of bisphosphonate- metal cation chelation of Mg²⁺/Ca²⁺/Sr²⁺ through the O- of two PO₃ (phosphonate) groups covalently linked to carbon for six ligands of 5AEL,5AFX,4QPF,3DYG,2F92 and 2I19. 

Scheme 2 Drug delivery of (5,5) armchair-SWCNT jointed with bisphosphonate agents of 5AEL, 5AFX,4QPF, 3DYG, 2F92, 2I19 chelated with Mg²⁺, Ca²⁺, Sr²⁺ in the bone of human body. 

The chelation of bisphosphonate agents of 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 with Mg²⁺, Ca²⁺, Sr²⁺ has been investigated in this study by forming relatively stable drugs for adsorption onto (5,5) armchair CNT as a drug deliver (Scheme 2). Thus, a series of quantum theoretical approaches has been accomplished for finding the optimized coordination of [bisphosphonate-Mg²⁺, Ca²⁺, Sr²⁺- (5,5) armchair CNT] chelation with DFT method of computations using Gaussian09 program package (Figure 1) ^[30].

Figure 1 Adsorption of a) 5AEL, b) 5AFX, c) 4QPF, d) 3DYG, e) 2F92, f) 2I19 chelated with Ca²⁺ onto surface of (5,5) armchair CNT. 

THEORETICAL BACKGROUND AND COMPUTATIONAL METHOD

The density functional theory (DFT) is one of the most employed approximations of Hohenberg, Kohn and Sham, which permit the theoretical study of material properties ^[31]. DFT theory proves an advantageous method for predicting chemical systems, and in order to understand its similarities and differences to other computational methods employed.

In this study, the geometries were optimized at the framework of DFT using the three-parameter Becke's exchange ^[32],^[33] and Lee-Yang-Parr's correlation non-local functional ^[34],^[35], usually known as B3LYP method and basis sets of lnl2dz for metal cations of Mg²⁺, Ca²⁺, Sr²⁺ and 6-311+G(2d,p) for other atoms including H,C,N,O,F,P. Then, it has been described the electronic structure of adsorbed (5,5) armchair SWCNT by bisphosphonate agents of 5AEL, 5AFX,4QPF, 3DYG, 2F92, 2I19 chelated with Mg²⁺, Ca²⁺, Sr²⁺ for measuring physico-chemical properties (Figure 1).

In this investigation, the Onsager model has been accomplished that was developed by Frisch, Wong and Wiberg utilizes spherical cavities. Even though this implies a less accurate description of the solute-solvent interface, this approximation simplifies the evaluation of energy formatives in geometry optimizations, and frequency analysis. Moreover, Cramer and Truhlar improved this model at dipole level ^[36]-^[40]. In fact, a cavity must have a physical sense such as Onsager model, and has a mathematical ability as often happened in other descriptions of solvent impacts ^[41]. Specially, the cavity has to keep out the solvent and including its frontiers as the biggest probability part of the solute charge distribution ^[41].

Then, The gauge including atomic orbitals (GIAO) has been adopted to solve the gauge problem in the calculation of nuclear magnetic shielding for the complexes of 5AEL, 5AFX,4QPF, 3DYG, 2F92, 2I19 chelated with Mg²⁺, Ca²⁺, Sr²⁺ adsorbed onto (5,5) armchair SWCNT using density functional theory (DFT) calculations.

These new drugs have been used for new lower bone tendency of bisphosphonate drug design which is sufficient curing diseases identifying by abnormal bone resorption (4QPF). The progress of selective protein farnesyl transferase (FTase) and protein geranylgeranyl transferase (GGTase) inhibitors as anticancer therapeutic agents has explored 3DYG which is more efficient than current bisphosphonate drugs ^[42]. 2I19 is a solid-state (13)C, (15)N, and (31)P magic-angle sample spinning (MAS) NMR and quantum chemical study of several bisphosphonates as pure structures and bonded to FPPS for preparing data collection about side chain and phosphonate backbone protonation states when bind to the enzyme ^[43]. It has been indicated the consequences of many potential prenyl synthase inhibitors against Trypanosoma brucei farnesyl diphosphate synthase (TbFPPS) and against T. brucei, the causative agent of human African trypanosomiasis. 5AFX is one of the most powerful compounds lipophilic analogs of the bone resorption medication of zoledronate family ^[44]. 2F92 has been attained by solving the crystal structures of human farnesyl pyrophosphate synthase (FPPS) in its unliganded state, in complex with the nitrogen containing bisphosphonate (N-BP) medications of, alendronate, ibandronate, pamidronate, zoledronate which prepare a new achieving of the mechanism of FPPS catalysis and inhibition ^[45].

A type of linkage of molecules to metal ions is chelation which defines the presence of two or more coordinated bonds between a multiple bonded ligand that are known chelating or sequestering agents and a single central metal atom. Chelation can be used between drugs and metal ions. For example, antibiotic drugs of the tetracycline and quinolone families are chelating agents of Fe²⁺, Ca²⁺, and Mg²⁺ ions ^[46],^[47].

The chelation of bisphosphonates with cations in bone cells has been accomplished in this research by forming relatively stable complexes. Therefore, a group of quantum theoretical methods has been run for exploring the optimized structures of [bisphosphonate-cations of Mg²⁺/Ca²⁺/Sr²⁺] cluster chelation adsorbed onto the surface of (5,5) armchair SWCNT as the drug delivery method in human bone with thermodynamic calculations and nuclear magnetic resonance analysis using Gaussian 09 program software ^[30],^[48].

RESULTS AND DISCUSSION

CNTs are representing drug delivery platforms that can be functionalized with various biomolecules including antibodies, proteins, and DNA. This permits the particular targeted for transferring the special tissues, organs, or cells. These compounds can easily penetrate cells, delivering drugs directly to the cytoplasm or nucleus. Drug delivery systems improve the pharmacological and therapeutic profile and efficacy of the drug and lower the occurrence of off-targets.

NMR analysis

The NMR data of isotropic (σ_iso), anisotropic shielding tensor (σ_aniso), and eigenvalues of chemical shielding including σ₁₁, σ₂₂, σ₃₃ for 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 adsorbed onto (5,5) armchair SWCNT, respectively, have been estimated (Table 1).

Table 1 SCF GIAO Magnetic shielding tensor for 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 in ppm chelated with cations at the adsorption site onto (5,5) armchair SWCNT. 

The computed results have indicated the SCF GIAO Magnetic shielding tensor in ppm for oxygen, nitrogen, fluorine, and phosphorus exploring the active site of 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 complexes of bisphosphonate agents as the drugs for osteoporosis and similar diseases cure. The calculations have been accomplished based on B3LYP/6-311+G (2d,p) level of theory using Gaussian 09 program software ^[30] and reported in Table 1.

The agents of 5AEL, 4PF, 2F92, 2I19 have approximately shown the identical behavior for various atoms in the active sites of these compounds through the NMR properties (Figure 2a). The bisphosphonate agents of 3DYG, 5AFX have also the similar fluctuation in the magnetic shielding tensor (Figure 2b).

Moreover, the 13C-NMR measurements on 2F92 and 2I19 bisphosphonate agents have demonstrated the active sites of these compounds exploring the most electronegative atoms for adsorbed onto (5,5) armchair SWCNT which represent the maximal shift in TMS B3LYP/6-311+G(2d,p) (Figure 2c,d).

The CS tensors are yielded by the quantum chemical calculations in principal axes system to estimate the isotropic chemical-shielding (CSI) and anisotropic chemical-shielding (CSA):

CSI (ppm) = (σ₃₃+ σ₂₂ + σ₁₁)/3 (1)

CSA (ppm) = σ₃₃-(σ₂₂ + σ₁₁)/2 (2)

Besides, the Onsager model has influenced on the nuclear magnetic resonance data and chemical shielding of H,C,N,O,F,P atoms in 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 (Figures 2a, 2b). It has been indicated that oxygen atom in 5AEL, 4PF, 2F92, 2I19 (Figure 2a) and nitrogen atom in 3DYG, 5AFX (Figure 2b) has the most effect on the NMR shielding which direct us toward the active site for adsorption onto (5,5) armchair SWCNT.

Figure 2 The NMR plot of isotropic (σ_iso), anisotropic (σ_aniso) and eigenvalue shielding tensors (σ₁₁, σ₂₂, σ₃₃) calculated by level of theory B3LYP/6-311+G(2d,p) for a) 5AEL and similar behavior of 4PF; b) 3DYG and similar behavior for 5AFX in ppm adsorbed site onto (5,5) armchair SWCNT. c) TMS B3LYP/6-311+G(2d,p) for 2F92 , d) TMS B3LYP/6-311+G(2d,p) for 2I19. 

IR method

The infrared (IR) calculations have been accomplished for bisphosphonate agents adsorbed onto (5,5) armchair SWCNT using B3LYP method and basis sets of lnl2dz for metal cations of Mg²⁺, Ca²⁺, Sr²⁺ and 6-311+G(2d,p) for other atoms including H,C,N,O,F,P to obtain the more accurate equilibrium geometrical parameters, thermodynamic properties and data for each of the determined structure. The IR spectrum for each of two bisphosphonate agents of 2F92 and 2I19 has been seen in the frequency range about 300 cm^-1 - 4700 cm^-1 and 1000 - 4600 cm^-1, respectively (Figure 3). Figure 3a has shown the strongest allowed peaks about 350, 750, 1100, 4600 cm^-1 for 2F92 agent and Figure 3b has indicated the highest frequency at 2100, 2750, 3750, 3400 cm^-1 for 2I19, respectively.

Figure 3 Calculated IR intensity (km/mol) versus frequency (cm^-1) through the IR spectra for a) 2F92 and b) 2I19 of bisphosphonate agents adsorbed onto (5,5) armchair SWCNT using 6-311+G(2d,p) calculations. 

The perspective of Figure 3 recommends the reason for existing observed various results of [5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19- Mg²⁺/Ca²⁺/Sr²⁺] complex chelation adsorbed onto (5,5) armchair SWCNT which present the position of active cites of labeled nitrogen, phosphorus, oxygen, fluorine, and metal cations of magnesium, calcium and strontium in these molecules which move the charge of electrons in polar bisphosphonates toward (5,5) armchair carbon nanotube.

Table 2 Calculated functions of harmonic frequencies (cm^-1), IR intensities (km/mol) in different normal modes; thermodynamic properties of ∆G, ∆H in kcal/mol and ∆S in cal/mol.K^-1 at 300 K and optimized energy of UV-Vis. 

Figure 3 demonstrates the relationship between intensity and frequency of 2F92 and 2I19 bisphosphonate agents in different normal modes of sharp peaks at B3LYP/6-311+G(2d,p) method. The calculations of the relative harmonic frequencies, IR intensities, and ΔH, ΔG, ΔS for active points of Pyridine and four derivatives of 4QPF, 2F92, 2I19 proteins have been reported in Table 2 and plotted in Figures 3 and 4.

It has been notable that polarization functions into the applied basis set in the computations always exist a significant achievement on the simulation and modeling methods of theoretical levels. The normal mode of spectra is exploring of harmonic potential wells by analytic methods which keep the movement of all atoms at the same time in the vibration time scale leading to a natural definition of molecular vibrations (Figure 4).

Figure 4 Calculated IR intensity (km/mol) versus frequency (cm^-1) for 4QPF bisphosphonate agent adsorbed onto (5,5) armchair SWCNT using 6-311+G(2d,p) calculations. 

Therefore, the physico-chemical properties of relative energy (kcal/mol), virial coefficient (-V/T) and dipole moment (Debye) have determined the stability of bisphosphonate agents among [5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19- Mg²⁺/Ca²⁺/Sr²⁺] complex chelation adsorbed onto (5,5) armchair SWCNT as the drugs for preventing the loss of bone cells, cure osteoporosis and other related diseases through the chelated bonding of these compounds with metal cations of Mg²⁺, Ca²⁺ and Sr²⁺ using the drug design method (Table 3 and Figure 5).

The calculated properties describe solubility and permeability for selected bisphosphonates through biological membranes that appear as efficient bioavailability indicators of investigated bisphosphonates, which can be a sufficient methodology to consider in Biopharmaceutical Classification System (BCS) progress.

Table 3 Thermo-physical characteristics of chelated agents of 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 with metal cations of Mg²⁺, Ca²⁺ and Sr²⁺ adsorbed onto (5,5) armchair SWCNT at 300 K. 

Figure 5 has exhibited that the six atoms of oxygen in each site of the bisphosphonate agents chelated to metal cations of Mg²⁺, Ca²⁺, Sr²⁺ in 5AEL, 5AFX, 4QPF, 3DYG, 2I19, 2F92 drugs have been minimized by ab-initio method using DFT level which includes ECP calculations with theoretical levels of LANL2DZ for metal elements.

Strontium (Sr) is known for its capability to increase bone and teeth mineralization, osteogenesis, and angiogenesis and downgrading osteoclast activity. This element as one of the main compounds of the bone tissues has a direct impact on metabolism of the bone. For improving bone cure, various investigations have concentrated on the substitution of calcium ions by strontium ions in the structure of bioactive glasses, which can be used for cure of vertebral complex fractures.

The results of the above observations strongly suggest that the different data observed of 5AEL, 5AFX, 4QPF, 3DYG, 2I19, 2F92 in the solvent is predominantly due to basis set functions are induced by a change in polarity of the environment. It is clear that an increase in the dielectric constants increases the stability and efficiency of these bisphosphonate drugs for preventing the loss of bone density and osteoporosis remedy ^[49]-^[53].

Figure 5 a) Relative energy versus Virial coefficient (-V/T) b) Dipole moment changes for chelated agents of 5AEL, 5AFX, 4QPF, 3DYG, 2F92, 2I19 with metal cations of Mg²⁺, Ca²⁺ and Sr²⁺ adsorbed onto (5,5)-SWCNT. 

CONCLUSION

Bisphosphonate agents have attracted much attention for the clinical treatment of some skeletal diseases depicted by enhancing of osteoclast-mediated bone resorption. According to this research, by incorporation of chelated magnesium, calcium and strontium ions to bisphosphonate drugs adsorbed onto (5,5) armchair SWCNT, the network compaction would increase owing the larger atomic radius of strontium atom rather than calcium and magnesium, respectively. For improving bone cure, various investigations have concentrated on the substitution of calcium ions by strontium ions in the structure of bioactive glasses, which can be used for cure of vertebral complex fractures.