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Article

Carbon Nanotubes as Biosensors for Releasing Conjugated Bisphosphonates–Metal Ions in Bone Tissue: Targeted Drug Delivery through the DFT Method

by
Fatemeh Mollaamin
1,2,* and
Majid Monajjemi
3
1
Department of Food Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu 37100, Turkey
2
Department of Biology, Faculty of Science, Kastamonu University, Kastamonu 37100, Turkey
3
Department of Chemical Engineering, Central Tehran Branch, Islamic Azad University, Tehran 1477893855, Iran
*
Author to whom correspondence should be addressed.
C 2023, 9(2), 61; https://doi.org/10.3390/c9020061
Submission received: 27 February 2023 / Revised: 16 May 2023 / Accepted: 16 June 2023 / Published: 19 June 2023
(This article belongs to the Special Issue Carbon Nanohybrids for Biomedical Applications)
Browse Figures
Versions Notes

Abstract

:
Bisphosphonate (BP) agents have attracted much attention for their precise therapy in some skeletal maladies demonstrated by enhancing osteoclast-mediated bone resorption. In this work, the use of CAM-B3LYP/6-311+G(d,p)/LANL2DZ to estimate the susceptibility of single-walled carbon nanotube (SWCNT) for adsorbing alendronate, ibandronate, neridronate, and pamidronate chelated to two metal cations of 2Mg2+, 2Ca2+, and 2Sr2+ through nuclear magnetic resonance and thermodynamic parameters has been accomplished. For most biological medications, oral bioavailability is too low to reach a therapeutic level, and advanced delivery systems such as formulations including permeation enhancers or enzyme inhibitors, lipid-based nanocarriers, and microneedles will likely increase the oral bioavailability of these medications properly. Therefore, the measurements have described that the eventuality of using SWCNT and BP agents becomes the norm in metal chelating of the drug delivery system, which has been selected through (alendronate, ibandronate, neridronate, pamidronate) → 2X (X = Mg2+/Ca2+/Sr2+) complexes. The NMR results of chelated alendronate, ibandronate, neridronate, and pamidronate complexes adsorbed onto (5,5) armchair SWCNT have remarked the location of active sites of tagged nitrogen (N), phosphorus (S), oxygen (O), and metal cations of magnesium (Mg2+), calcium (Ca2+), and strontium (Sr2+) in these molecules which replace the movement of the charge electron transfer in polar bisphosphonates (BPs) toward (5,5) armchair carbon nanotube (CNT). The thermodynamic results have exhibited that the substitution of 2Ca2+ cation by 2Sr2+ cation in the compound of the bioactive glasses can be efficient for treating vertebral complex fractures. However, the most fluctuation in the Gibbs free energy for BPs → 2Sr2+ has been observed at 300 K. This manuscript aimed to show that (5,5) armchair SWCNT can easily penetrate in the bone cells, delivering chelated BP–cations directly to the bone tissue. Drug delivery systems can improve the pharmacological profile, therapeutic profile, and efficacy of BP drugs and lower the occurrence of off-targets.

1. Introduction

The compounds of bisphosphonates (BPs) prevent the digestion of bones by pushing osteoclasts to bear cell death or apoptosis, which diminishes the velocity of bone destruction [1,2].
BP compounds stop bone resorption produced by different reasons in cells and organs. They prevent the formation of holes by isolating osteoclasts on mineral layers. The principal impact of active BPs is to prevent the resorption of bone tissue [3].
There is attention on enhancing the availability of biology and period of activity of a medication to modify remedial consequences. One of the applications of nanotechnology is in drug delivery, where nanoparticles are applied to carry and release drugs to a specific zone in the body. Targeted drug delivery is the delivery of a drug to its target site without having an effect on other tissues. Interest in targeted drug delivery has grown drastically due to its potential implications in the treatment of cancers and other chronic diseases. In order to achieve efficient targeted delivery, the designed system must avoid the host’s defense mechanisms and circulate to its intended site of action. This drug delivery technique is able to change the pharmacology and particularity of a medication by adjusting it with various ingredients, medication carriers, and medical equipment [4].
BPs prevent the establishment, postpone the association, and decrease the solution of Ca3(PO4)2 compounds. This notable characteristic is the foundation for the employment of these structures as a sign of the functionalized skeleton in nuclear medical sciences and the basis for their chosen localization in the bone tissue when employed as drugs [5,6,7,8,9,10,11,12,13,14]. The compounds of nanomedicine support a vast span of remedial demands, from nano drug delivery technology containing carbon nanostructures and the two-layered hydroxide to biological sensors in vitro and visualizing and implanting instruments in vivo through accurate diagnostics [15,16,17,18,19,20,21,22,23].
As shown by the exploration of CNTs in the 1990s and the progress of their applications in nanomedicine, these compounds possess significant properties, including rich electronic and thermal factors, great mechanical rigidity, high chemical resistance, and extremely light in weight [24,25,26,27,28,29].
The structures of nanotubes (NTs) with their natural attributes have been thought powerful applicants for drug delivery systems. The existence of capped ends of NTs might be opened up by oxidation, permitting the adhesion of molecules concerned with entry into the NT. Carbon nanotubes (CNTs) could lightly enter cells, releasing drugs straight into the nucleus or cytoplasm [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46].
As a matter of fact, the most popular BP medications have a rich tension for metal cations, among them calcium cations, with which they can generate both soluble and insoluble compounds and aggregates relating to the pH of the solution and the existing metal [47,48,49,50,51,52,53].
Non-N-consisting BPs, such as clodronate, etidronate, and tiludronate, are discussed as the first generation of BPs, which are simple molecules including single atoms or alkyl groups in R1 and R2 side chains having a weak inhibition impact on bone resorption [54].
Adding an amino group introduced the start of the second generation of BPs that were more powerful, such as pamidronate as the first one, and other identical ones were pursued, where the situation of the nitrogen in the side chain was the clue to a more efficient medication [55].
Currently, the third generation of BPs, including N-containing heterocyclic BPs such as zoledronate and risedronate, have been presented. They have displayed the strongest antiresorptive attributes [56,57]. During the past years, the third generation of BPs with enhancing bone affinity has been brought up for osteoporosis and other bone disease treatments [58,59,60].
In this article, four second-generation BP agents containing alendronate, ibandronate, neridronate, and pamidronate, which have nitrogen (N) atoms in the side chain of R2 for promoting osteoclast apoptosis, have been investigated.
Alendronic acid (C4H13NO7P2) inhibits osteoclast-mediated bone resorption. Healthy bone tissue under therapy expands, and alendronate remains in the matrix of bone cells as an inactive pharmaco-figure. The best activity demands enough Ca element and vitamin D in the body to develop wholesome bone tissue [61,62,63].
Ibandronic acid (C9H23NO7P2) is also a second-generation BP medication, which is applied in the prohibition of and cures osteoporosis and deformation accompanied by skeletal fractures with cancer malady. It might likewise be employed to cure the increase in blood calcium levels in hypercalcemia [64,65].
Neridronic acid (C6H17NO7P2) is in a class of BP medications which is applied to cure imperfect osteogenesis and Paget’s illness of bone cells [66,67].
Pamidronic acid (C3H11NO7P2) is another N-containing BP employed to prohibit osteoporosis and strengthen bones in Paget’s disease. It is also employed to prevent bone loss, owing to steroid application, and in some cancers with high orientation to bone such as multiple myeloma. Due to its susceptibility to sequester Ca element in bone tissue, it is also applied to cure high amounts of Ca element and complex regional pain syndrome [68,69].
In this work, the chelation of BP agents of alendronate, ibandronate, neridronate, and pamidronate with 2Mg2+, 2Ca2+, and 2Sr2+ have been investigated in aqueous medium by forming relatively stable drugs for adsorption onto (5,5) armchair CNT as a drug delivery system (Scheme 1).
Then, a group of applied methods in quantum chemistry has been performed for detecting the optimum symmetry of [BP → 2Mg2+, 2Ca2+, 2Sr2+—(5,5) armchair CNT] chelation with the DFT method of computations using Gaussian 16 revision C.01 program package [70].

2. Design, Material, and Methods

In this investigation, the coordination geometries have been minimized at the insight of density functional theory by applying the three-parameter Becke’s exchange [71] and Lee–Yang–Parr’s correlation non-local functional [72], generally nominated as B3LYP method and basis sets of LANL2DZ by using Gaussian 16 revision C.01 program package [70] for two metal cations of Mg2+, Ca2+, and Sr2+ and 6-311+G(2d,p) for other atoms, including H, C, N, O, F, and P. Then, the electronic structure of adsorbed (5,5) armchair SWCNT by BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ for measuring physico-chemical properties was described (Scheme 1).
DFT is one of the most employed approximations of Hohenberg, Kohn, and Sham, which permits the computational research of material attributes [73]. This theoretical method approves a beneficial system for estimating chemical mechanisms and understanding its resemblances and diversities to other computational applied approaches [74,75,76,77].
Moreover, the Onsager figure, progressed by Frisch, Wong and, Wiberg utilizing spherical cavities, has been accomplished. Although this method indicates a less detailed statement of the solute–solvent interface, this approximation simplifies the assessment of energy formatives in geometry coordination and frequency analysis. Furthermore, Cramer and Truhlar improved this pattern at the dipole surface [78,79,80,81,82,83].
Therefore, GIAO or the gauge including atomic orbitals has been accorded to work out the gauge problem in the computation of nuclear magnetic shielding for the complexes of alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ adsorbed onto (5,5) armchair SWCNT using DFT perspectives.
The chelation of BPs with cations in bone tissues was accomplished in this research by creating relatively stable complexes. Therefore, a group of quantum theoretical methods has been run to explore the minimized structures of [BP → 2Mg2+/2Ca2+/2Sr2+] cluster chelation adsorbed onto the surface of (5,5) armchair SWCNT as the drug delivery method in human bones, with thermodynamic calculations and nuclear magnetic resonance analysis using Gaussian 16 revision C.01 program [70,84,85,86].

3. Results

CNTs represent drug delivery platforms that can be functionalized with various biomolecules, including antibodies, proteins, and DNA. This permits the particular targeted transferring to special organs, cells, or tissues [87].

3.1. NMR Analysis

The computed results extracted from nuclear magnetic resonance (NMR) have indicated the SCF GIAO magnetic shielding tensor in ppm for oxygen, nitrogen, phosphorus, magnesium, calcium, and strontium exploring the active sites of alendronate, ibandronate, neridronate, and pamidronate complexes of BP agents as the medications for osteoporosis and analogous maladies cure. The calculations have been accomplished based on CAM-B3LYP/6-311+G (2d,p) order of theoretical computations due to Gaussian 16 revision C.01 software [70] and reported in Table 1.
The shielding parameters of NMR spectroscopy consisting of isotropic (σiso) and anisotropic tensors (σaniso) for alendronate, ibandronate, neridronate, and pamidronate chelated to metal cations of 2Mg2+, 2Ca2+, and 2Sr2+, which have been adsorbed onto (5,5) armchair SWCNT, have been estimated in Table 1.
In the aqueous medium, the agents of alendronate, ibandronate, neridronate, and pamidronate chelated to metal cations of 2Mg2+, 2Ca2+, and 2Sr2+ adsorbed onto (5,5) armchair SWCNT have approximately shown identical behavior for diverse atoms in the active zones of these complexes through the NMR qualities (Figure 1).
Alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+ have two sharp fluctuations in anisotropic shielding for oxygen atoms, while a steady state for other atoms, and especially for magnesium atoms (Figure 1a). Moreover, these BP agents chelated to 2Ca2+ have two sharp fluctuations in anisotropic shielding for oxygen atoms and a steady state for other atoms, while sharp peaks for calcium atoms have been observed (Figure 1b). Strontium atoms have shown sharp peaks through chelating to four mentioned BP units of osteoporosis drug (BP → 2Sr2+) using NMR anisotropic shielding (Figure 1c). The CS tensors are yielded by the quantum chemical calculations in fundamental axes system to estimate the isotropic chemical shielding (CSI), (σ33 + σ22 + σ11)/3, and anisotropic chemical shielding (CSA), σ33 – (σ22 + σ11)/2 [88].
In addition, the Onsager model has influenced NMR traits and shielding tensors of H, C, N, O, P, Mg, Ca, and Sr atoms in chelated alendronate, ibandronate, neridronate, and pamidronate (Figure 2). In the results of 1H-NMR spectroscopy in Figure 2, the fluctuation of chemical shielding using nuclear magnetic resonance for these chelated BPs is shown.
As a matter of fact, alendronate, ibandronate, and neridronate have shown NMR shielding between 10–1400 ppm with a sharp peak in 25 ppm and several weak peaks between 200–400 ppm (Figure 2a–c). Pamidronate has NMR shielding between 10–600 ppm with a sharp peak in 25 ppm and several weak peaks between 200–400 ppm (Figure 2d).
In addition, in Figure 2a–d, an electrostatic potential (ESP) surface or map of a molecule that presents the partial distribution of change along the molecule’s surface, which helps to assign molecular polarity, has been shown.
The outlook of Figure 2 suggests the proof for standing a variety of measurements for chelated alendronate, ibandronate, neridronate, and pamidronate complexes adsorbed onto (5,5) armchair SWCNT, which presents the location of active zones of targeted atoms of N, P, O, and metal cations of Mg2+, Ca2+, and Sr2+ in these molecules that replace the charge transfer factor in polar BPs toward (5,5) armchair CNT.

3.2. Nuclear Quadrupole Resonance (NQR)

In NMR, nuclei with spin ≥ 1/2 have a magnetic dipole moment so that their energies are split by a magnetic field, permitting resonance sorption of energy dependent on the Larmor frequency;   ω L = γ B , where γ is the gyromagnetic ratio and B is the magnetic field external to the nucleus.
As the electric field gradient (EFG) at the position of the nucleus in organic inhibitors is assigned by the valence electrons twisted in the special linkage with close nuclei of aluminum surface, the NQR frequency at which transitions happen is particular for BPs (alendronate/ibandronate/neridronate/pamidronate) → 2X (X = Mg2+/2Ca2+/2Sr2+) complexes in aqueous medium (Table 2).
Moreover, the electric potential through transferring of electric charge from one site to another site in the presence of an electric field has been measured for BPs (alendronate/ibandronate/neridronate/pamidronate) → 2X (X = Mg2+/Ca2+/Sr2+) complexes using CAM-B3LYP/EPR-III, 6-31+G(d,p), LANL2DZ level of theory (Figure 3). Therefore, in Figure 3, the electric potential of the NQR method for elements of C, O, N, P, Mg, Ca, and Sr dealing with interaction sites between BPs and chelated metallic cations in aqueous medium has been plotted.
There is an electric quadrupole moment in NQR, nuclei with spin ≥ 1, which is accompanied by non-spherical nuclear charge distributions. So, the nuclear charge repartition digresses from that of a sphere as the oblate or prolate form of the nucleus [89,90].
Therefore, the NQR transition frequencies are symmetric to the electric quadrupole moment of the nucleus and the scale of the strength of the local EFG: ω   ~   e 2   Q q ħ   = C q , where q is dependent on the biggest fundamental portion of the EFG tensor at the nucleus, and C q is the quadrupole coupling constant parameter [89,90].
The NQR method is based on the multipole expansion in Cartesian coordinates as the following equations:
V r = V 0 + ∂ V ∂ x i | 0   · x i + 1 2 ∂ 2 V ∂ x i x j | 0 · x i x j + ⋯  
Then, after simplification of the equation, there are only the second derivatives dependent on the same variable for the potential energy [89,90,91,92]:
U = − 1 2     ∫ D d 3   r   ρ r ∂ 2 V ∂ x i 2 | 0 · x i 2 = − 1 2     ∫ D d 3   r   ρ r ∂ E i ∂ x i | 0 · x i 2 = − 1 2   ∂ E i ∂ x i 0 · ∫ D d 3   r   ρ r · x i 2
The effect of the substitution of metal cations of 2Mg2+/2Ca2+/2Sr2+ chelated to BPs adsorbed onto (5,5) armchair SWCNT through resulted electric potential using NQR analysis (Table 2 and Figure 3) has been observed. It is obvious that the graph of NQR characteristics for BPs (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ has the most fluctuation in the region of magnesium, calcium, and strontium (Figure 3).

3.3. Physical and Thermochemical Properties

The physical and chemical properties of dipole moment (Debye), Virial coefficient (-V/T), relative energy (kcal/mol), and Gibbs free energy (kcal/mol) have determined the stability of BP agents among the chelated BPs, including alendronate/ibandronate/neridronate/pamidronate → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT as the medications for excluding the damage of bone tissues and curing osteoporosis and other relevant maladies through the chelated bonding of these complexes with Mg2+, Ca2+, and Sr2+ using the drug delivery procedure (Table 3).
Figure 4 has exhibited that the fluctuation of relative energy in front of the Virial coefficient (-V/T) for BPs of alendronate/ibandronate/neridronate/pamidronate chelated to 2Mg2+, 2Ca2+, 2Sr2+ adsorbing onto (5,5) armchair SWCNT in aqueous medium, which was optimized by ab initio approach accompanying CAM-DFT functional consisting of ECP computations with theoretical status of LANL2DZ for metal elements.
In Figure 4, it has been observed that with increasing Virial coefficient, the relative energy for (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT is reduced, with a relation coefficient of R2 = 0.9088.
The observed consequences strongly propose that the various measurements derived from BP agents in the solvent are mainly because basis sets are persuaded by an alteration in the polarity of the ambience. It is obvious that an enhancement in the dielectric constants augments the resistance and efficiency of these BP medications for prohibiting the damage of bone density and remedying osteoporosis (Figure 5).
Strontium (Sr) is famous for its capability to increase bone and teeth mineralization, osteogenesis, and angiogenesis and downgrade osteoclast activity. This element, as one of the principal compounds of bone tissue, has a straight impact on the metabolism of the bone. For improving bone treatments, various investigations have concentrated on the exchange of Ca2+ cations by strontium ions in the compound of bioactive glasses, which can be used to cure vertebral complex fractures [93,94]. In Figure 5, BPs chelated to strontium (Sr) have shown the most fluctuation in Gibbs free energy with dipole moments in the aqueous medium at 300 K.
From Figure 5, the minimum values based on Δ G R o versus dipole moment might relate to the interactions between the chelated BP structures in the aqueous medium and the CNT surface. In fact, by comparing to Δ G R o amounts, an acceptable accord among computed consequences has been approved, as well as the accuracy of the chosen isotherm for (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium, which is approved by the following equation:
Δ G R o = Δ G B P s − 2 X 2 + →   C N T o − Δ G B P s     o + Δ G 2 X 2 +     o + Δ G   C N T     o ;   X = M g , C a ,   S r
On the basis of data in Table 3, it is predicted that the adsorption of BPs-2X2+ (X = Mg, Ca, Sr) on the CNT may be physical or chemical in nature. As seen in Table 3, all the evaluated Δ G R o amounts are mostly close, exhibiting the settlement of the figured parameters by all approaches and the reliability of the measurements.

3.4. LUMO and HOMO (Frontier Orbital)

The frontier orbitals of LUMO and HOMO as the lowest unoccupied molecular orbital and highest occupied molecular orbital, respectively, have been calculated for BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ adsorbing onto (5,5) armchair SWCNT in aqueous medium accompanying CAM-B3LYP/6-31+G (2d,p), EPR-III, LANL2DZ (Table 4).
LUMO, HOMO, and band energy gap (ev) indicated the pictorial explanation of the frontier molecular orbitals, which are an important factor for identifying the molecular characteristics of the drug delivery method though adsorbing the BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+, which have been surrounded by H2O molecules on the (5,5) armchair SWCNT in aqueous medium (Figure 6).
In this research, the energy gap appoints how BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ can interact with (5,5) armchair SWCNT in aqueous medium. In addition, to attain more decisive approval in recognizing the specification of complexes of this structure, a group of chemical reactivity factors consisting of chemical potential (µ), electronegativity (χ), hardness (η), softness (ζ), and electrophilicity index (ψ) have been included (Table 4) [95,96,97]. The amounts of the parameters in Table 4 have exhibited good stability of BP agents through Langmuir adsorption on the (5,5) armchair SWCNT.
Molecular interactions are often related to the interaction energies, which, in turn, decide the Gibbs free energy of the incorporation of CNTs in the intercellular cavities. Moreover, hydrogen bonds play a vital role in the solubility of CNTs. Functionalization and composite formation with polymers increase the hydrogen bonding sites. Hydrogels help to increase the hydrophilicity of CNTs. As the number of hydrogen bonds increases, the solubility increases, which is essential for the interaction of CNTs with (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ drugs. Although SWCNT might have higher interaction energy from van der Waals forces with chelated BPs with two metal cations 2Mg2+, 2Ca2+, and 2Sr2+ that can make them highly stable, the low electric potential extracts from electrostatic properties of NQR (Table 2 and Figure 3) for elements of BPs → 2Mg2+/2Ca2+/2Sr2+ in the aqueous medium, which have been adsorbed on the SWCNT surface, can indicate that van der Waals (vdW) energies might be neglected.

4. Conclusions

According to this research, by the incorporation of chelated 2Mg2+, 2Ca2+, and 2Sr2+ cations to BP drugs adsorbed onto (5,5) armchair SWCNT, the lattice compression would increase, owing to the larger atomic radius of Sr2+ cation rather than Ca2+ and Mg2+, respectively.
The perspective of NMR spectroscopy has suggested the location of active sites of targeted N, P, O, and two metal cations of 2Mg2+, 2Ca2+, and 2Sr2+ in chelated alendronate, ibandronate, neridronate, and pamidronate complexes adsorbed onto (5,5) armchair SWCNT replaces the charge density in polar BPs in the aqueous medium toward (5,5) armchair CNT. For improving bone treatments, various investigations have concentrated on the substitution of 2Ca2+ cation by 2Sr2+ cation in the compound of bioactive glasses, which can be used for curing vertebral complex fractures.
Compared to Δ G R o amounts from infrared spectroscopy, an appropriate accord among computed consequences has been approved, as well as the accuracy of the chosen isotherm for (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium, with the most fluctuation in Gibbs free energy for BPs → 2Sr2+ at 300 K. In fact, the achieved results represented the feasibility of using (5,5) armchair SWCNT, and these compounds became the norm in the drug delivery system, which was attained by quantum calculations due to the physico-chemical properties of NMR and IR spectroscopies [98]. Finally, this work has approved that SWCNT can penetrate bone cells for the release of chelated BP–cations directly to bone tissue, which is based on a drug delivery method towards improving the pharmacological and therapeutic system.

Author Contributions

F.M.: Conceptualization and idea, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing—original draft preparation, Visualization, Supervision, Project administration. M.M.: Methodology, Software, Formal analysis, Investigation, Data curation, Writing—review and editing, Visualization, Resources. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Acknowledgments

In successfully completing this paper and its research, the authors are grateful to Kastamonu University for support through the office, library, and scientific websites.

Conflicts of Interest

The authors declare no conflict of interest.

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Carbon 09 00061 sch001 550
Scheme 1. Drug delivery of BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated (top-middle) with regarding the Ramachandran Plot (bottom-left) to metal cations 2Mg2+, 2Ca2+, and 2Sr2+ (top-right) using (5,5) armchair SWCNT in aqueous medium (bottom-right) with for the treatment of osteoporotic bones (top-left) in the human body.
Scheme 1. Drug delivery of BP agents of alendronate, ibandronate, neridronate, and pamidronate chelated (top-middle) with regarding the Ramachandran Plot (bottom-left) to metal cations 2Mg2+, 2Ca2+, and 2Sr2+ (top-right) using (5,5) armchair SWCNT in aqueous medium (bottom-right) with for the treatment of osteoporotic bones (top-left) in the human body.
Carbon 09 00061 sch001
Carbon 09 00061 g001 550
Figure 1. 13C-NMR shielding of isotropic (σiso) and anisotropic (σaniso) tensors calculated for (a) BPs-Mg2+, (b) BPs-Ca2+, and (c) BPs-Sr2+ using the SCF GIAO method due to CAM-B3LYP function and LANL2DZ basis set for metal cations and 6-311+G(2d,p) basis set for further atoms through electronegative atoms of N, O, and P as the active positions in the structures of BP agents.
Figure 1. 13C-NMR shielding of isotropic (σiso) and anisotropic (σaniso) tensors calculated for (a) BPs-Mg2+, (b) BPs-Ca2+, and (c) BPs-Sr2+ using the SCF GIAO method due to CAM-B3LYP function and LANL2DZ basis set for metal cations and 6-311+G(2d,p) basis set for further atoms through electronegative atoms of N, O, and P as the active positions in the structures of BP agents.
Carbon 09 00061 g001
Carbon 09 00061 g002a 550Carbon 09 00061 g002b 550
Figure 2. 1H-NMR shielding and ESP map of (a) alendronate-X2+, (b) ibandronate-X2+, (c) neridronate-X2+, and (d) pamidronate-X2+ using the SCF GIAO method due to B3LYP function and lnl2dz basis set for metal cations (X2+), including Mg2+, Ca2+, and Sr2+,and 6-311+G(2d,p) basis set basis set for alternative atoms.
Figure 2. 1H-NMR shielding and ESP map of (a) alendronate-X2+, (b) ibandronate-X2+, (c) neridronate-X2+, and (d) pamidronate-X2+ using the SCF GIAO method due to B3LYP function and lnl2dz basis set for metal cations (X2+), including Mg2+, Ca2+, and Sr2+,and 6-311+G(2d,p) basis set basis set for alternative atoms.
Carbon 09 00061 g002aCarbon 09 00061 g002b
Carbon 09 00061 g003 550
Figure 3. The changes of the electric potential versus atomic charge through NQR calculations for BPs (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ in aqueous medium adsorbed on the SWCNT surface by CAM-B3LYP/EPR-III,6-31+G(d,p), LANLD2Z calculations extracted from the NQR method (Note: X = Mg/Ca/Sr).
Figure 3. The changes of the electric potential versus atomic charge through NQR calculations for BPs (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ in aqueous medium adsorbed on the SWCNT surface by CAM-B3LYP/EPR-III,6-31+G(d,p), LANLD2Z calculations extracted from the NQR method (Note: X = Mg/Ca/Sr).
Carbon 09 00061 g003
Carbon 09 00061 g004 550
Figure 4. Changes of relative energy versus Virial coefficient (-V/T) for chelated BP agents with two metal cations of Mg2+, Ca2+, and Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
Figure 4. Changes of relative energy versus Virial coefficient (-V/T) for chelated BP agents with two metal cations of Mg2+, Ca2+, and Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
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Carbon 09 00061 g005 550
Figure 5. The changes of Gibbs free energy   ( Δ G R o ) (kcal/mol) versus dipole moment (Debye) for chelated BP agents with two metal cations of Mg2+, Ca2+, and Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
Figure 5. The changes of Gibbs free energy   ( Δ G R o ) (kcal/mol) versus dipole moment (Debye) for chelated BP agents with two metal cations of Mg2+, Ca2+, and Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
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Carbon 09 00061 g006 550
Figure 6. The energy gap of HOMO/LUMO (a.u.) for adsorbing alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ onto (5,5) armchair SWCNT in aqueous medium.
Figure 6. The energy gap of HOMO/LUMO (a.u.) for adsorbing alendronate, ibandronate, neridronate, and pamidronate chelated to 2Mg2+, 2Ca2+, and 2Sr2+ onto (5,5) armchair SWCNT in aqueous medium.
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Table
Table 1. SCF GIAO magnetic shielding tensor for alendronate, ibandronate, neridronate, and pamidronate in ppm chelated to metal cations of 2Mg2+, 2Ca2+, and 2Sr2+ at the adsorption site onto (5,5) armchair SWCNT in aqueous medium.
Table 1. SCF GIAO magnetic shielding tensor for alendronate, ibandronate, neridronate, and pamidronate in ppm chelated to metal cations of 2Mg2+, 2Ca2+, and 2Sr2+ at the adsorption site onto (5,5) armchair SWCNT in aqueous medium.
Alendronate → 2Mg2+
ppmP2O3P4O5O6O7O8N14Mg15Mg16
σiso476.9364354.2408526.9666201.1994417.9254272.9464338.2907295.2486476.8934449.8215
σaniso197.315394.4458209.7908927.36991271.225109.11001160.476032.8868273.6673317.7684
Alendronate → 2Ca2+
ppmP2O3P4O5O6O7O8N14Ca15Ca16
σiso560.1002352.9742533.0987133.3365238.4170122.0996273.4535299.23741266.89351242.6875
σaniso144.200163.4751247.7018359.3426291.6360636.0180369.222932.2780190.3530186.0608
Alendronate → 2Sr2+
ppmP2O3P4O5O6O7O8N14Sr15Sr16
σiso578.0939398.6744560.6582378.7838392.6713389.2691392.7619299.58703153.59583230.1562
σaniso184.704569.5146177.8449205.3841221.1451243.9178248.887928.5730257.5701204.4964
Ibandronate → 2Mg2+
ppmO1P3O4O5O6P7O8N13Mg19Mg20
σiso362.9223418.106559.974034.3478138.1868424.744336.0918293.6687537.7617523.1200
σaniso57.8641147.7471487.9605510.3891728.4770174.0288439.929438.7725159.6272203.9691
Ibandronate → 2Ca2+
ppmO1P3O4O5O6P7O8N13Ca19Ca20
σiso361.5829210.1687452.6134669.4192677.6753349.5293187.1626293.19901221.73901150.9306
σaniso57.0125394.71861378.50361425.40721457.4494227.4777899.290240.5514199.6107372.1082
Ibandronate → 2Sr2+
ppmO1P3O4O5O6P7O8N13Sr19Sr20
σiso365.6022331.3843317.9684408.4177228.0619426.3955120.2419292.78503130.94513039.3312
σaniso69.4799209.73311123.97181191.6414831.624498.9009819.378440.7449250.0123505.0866
Neridronate → 2Mg2+
ppmO1P3O4O5O6P7O8N16Mg17Mg18
σiso362.0412411.782940.149888.5579183.8948435.266343.0977298.1960528.3357534.3457
σaniso57.1142162.3461533.2377448.0810788.6783107.3363452.005629.1476183.6469184.4351
Neridronate → 2Ca2+
ppmO1P3O4O5O6P7O8N16Ca17Ca18
σiso361.1504295.8674284.3469313.0876419.9667375.6348181.9129297.50331183.24411202.8418
σaniso55.2182263.48521198.83841051.25971099.8941177.8481875.283329.3969288.6887231.3930
Neridronate → 2Sr2+
ppmO1P3O4O5O6P7O8N16Sr17Sr18
σiso367.1523390.606840.03239.2850152.4282390.919032.2100298.4373 3061.40673101.5619
σaniso73.7996126.9946858.7106697.0640720.7286138.6716689.590130.3294246.8092175.3476
Pamidronate → 2Mg2+
ppmO1P3O4O5O6P7O8N13Mg14Mg15
σiso362.0592381.045566.954129.6460279.2352403.38518.7584298.0285522.9221515.9499
σaniso61.9317198.8411474.8645486.8028909.1096153.6341465.753929.4898201.9489227.1125
Pamidronate → 2Ca2+
ppmO1P3O4O5O6P7O8N13Ca14Ca15
σiso363.4157308.7031139.8592313.4116335.8527302.3324368.3457298.70441180.34161195.3529
σaniso55.7660229.5383992.3576852.3174963.5384253.4179812.823630.5223259.1125268.9893
Pamidronate → 2Sr2+
ppmO1P3O4O5O6P7O8N13Sr14Sr15
σiso363.8761241.3363515.8675557.2093446.4313382.1276109.8785296.77193017.45053053.8428
σaniso65.8230339.83841283.11541420.81031145.4648144.3417846.585231.5079558.2663370.8348
Table
Table 2. The electric potential for elements of BPs → 2Mg2+/2Ca2+/2Sr2+ in aqueous medium that have been adsorbed on the SWCNT surface by CAM-B3LYP/EPR-III,6-31+G(d,p), LANL2DZ calculations extracted from the NQR method.
Table 2. The electric potential for elements of BPs → 2Mg2+/2Ca2+/2Sr2+ in aqueous medium that have been adsorbed on the SWCNT surface by CAM-B3LYP/EPR-III,6-31+G(d,p), LANL2DZ calculations extracted from the NQR method.
Atom TypeAlendronate-2Mg2+Alendronate-2Ca2+Alendronate-2Sr2+Atom TypePamidronate-2Mg2+Pamidronate-2Ca2+Pamidronate-2Sr2+
C1−14.582015−14.680364−14.698286O1−22.089153−22.112109−22.145726
P2−53.374813−53.279858−53.29495C2−14.579306−14.602032−14.638223
O3−22.058521−22.149621−22.098919P3−53.406411−53.417423−53.477559
P4−53.376494−53.282896−53.27529O4−22.272632−22.279084−22.336336
O5−22.244579−22.278534−22.394044O5−22.258221−22.248791−22.343459
O6−22.229734−22.286302−22.390886O6−22.456859−22.462141−22.517174
O7−22.431022−22.429008−22.442474P7−53.376249−53.408809−53.453886
O8−22.239543−22.278605−22.412946O8−22.233854−22.239144−22.352915
O9−22.204363−22.27527−22.397572O9−22.229882−22.285782−22.304591
O10−22.40249−22.456515−22.473484O10−22.408516−22.432219−22.484225
C11−14.561176−14.600068−14.578144C11−14.564672−14.577927−14.601869
C12−14.543709−14.561792−14.530637C12−14.545795−14.572535−14.576751
C13−14.51357−14.520012−14.514399N13−18.152349−18.171899−18.160602
N14−18.130473−18.146224−18.128618X14−39.095005−79.482876−194.832492
X15−39.09341−79.466582−194.914058X15−39.061118−79.461646−194.815758
X16−39.093721−79.477353−194.90834
Atom TypeIbandronate-2Mg2+Ibandronate-2Ca2+Ibandronate-2Sr2+Atom TypeNeridronate-2Mg2+Neridronate-2Ca2+Neridronate-2Sr2+
O1−22.071174−22.090505−22.135028O1−22.063309−22.079958−22.162592
C2−14.55445−14.576253−14.627075C2−14.546229−14.565095−14.661299
P3−53.377051−53.398859−53.464651P3−53.378029−53.393132−53.507653
O4−22.232796−22.250951−22.326769O4−22.239304−22.250603−22.39611
O5−22.232416−22.226345−22.32228O5−22.234969−22.224863−22.37294
O6−22.410299−22.442602−22.498632O6−22.417286−22.426463−22.551375
P7−53.353291−53.373911−53.437238P7−53.324873−53.342394−53.469496
O8−22.219745−22.241599−22.327087O8−22.191646−22.214617−22.352985
O9−22.212105−22.212723−22.310918O9−22.19086−22.188493−22.348579
O10−22.383435−22.380158−22.417829O10−22.316029−22.340715−22.505319
C11−14.548019−14.564822−14.601757C11−14.539276−14.556356−14.627277
C12−14.53678−14.558542−14.589055C12−14.558729−14.581511−14.640502
N13−18.142608−18.152869−18.17498C13−14.539792−14.555941−14.587432
C14−14.514959−14.514147−14.525321C14−14.530353−14.543764−14.562173
C15−14.553135−14.541599−14.550868C15−14.505909−14.512938−14.524351
C16−14.547176−14.534201−14.545824N16−18.138051−18.139505−18.150542
C17−14.54458−14.532666−14.552941X17−39.064255−79.461993−194.854003
C18−14.542677−14.536273−14.550469X18−39.016632−79.412003−194.820676
X19−39.028844−79.428857−194.800917
X20−39.063707−79.469808−194.822286
Table
Table 3. Physico-chemical characteristics of chelated agents of BPs with each of two metal cations of Mg2+, Ca2+, and Sr2+, respectively, adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
Table 3. Physico-chemical characteristics of chelated agents of BPs with each of two metal cations of Mg2+, Ca2+, and Sr2+, respectively, adsorbed onto (5,5) armchair SWCNT in aqueous medium at 300 K.
BPs AgentMetal CationRelative Energy
×10−4 (kcal/mol)		Gibbs Free Energy ×10−4 (kcal/mol)Virial
Coefficient (-V/T)		Dipole Moment (Debye)
Alendronate2Mg2+−105.3238−208.34441.95765.0901
2Ca2+−157.7413−278.25091.91293.2620
2Sr2+−471.0163−632.85291.99995.2236
Ibandronate2Mg2+−101.7982−240.36871.823319.5703
2Ca2+−159.7855−315.84921.869122.2388
2Sr2+−482.5812−683.25212.003028.8543
Neridronate2Mg2+−102.8331−226.27521.878918.4846
2Ca2+−161.3368−301.33481.902120.1825
2Sr2+−471.6486−654.13301.990828.9546
Pamidronate2Mg2+−95.8092−195.24571.875416.0488
2Ca2+−164.3777−278.46101.972618.5122
2Sr2+−472.0945−624.28672.005234.5252
Table
Table 4. The LUMO (a.u.), HOMO (a.u.), band energy gap (∆E/ev), and other qualifications (ev) for (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium by CAM-B3LYP functional and 6-31+G (2d,p), EPR-III, LANL2DZ basis sets.
Table 4. The LUMO (a.u.), HOMO (a.u.), band energy gap (∆E/ev), and other qualifications (ev) for (alendronate/ibandronate/neridronate/pamidronate) → 2Mg2+/2Ca2+/2Sr2+ adsorbed onto (5,5) armchair SWCNT in aqueous medium by CAM-B3LYP functional and 6-31+G (2d,p), EPR-III, LANL2DZ basis sets.
Inhibitor → Al-AlloyHOMOLUMO∆EµχHζψ
Alendronate → 2Mg2+−0.11600.24859.91881.8027−1.80274.95940.10080.3276
Alendronate → 2Ca2+−0.10060.07074.6594−0.40680.40682.32970.21460.0355
Alendronate → 2Sr2+−0.10860.22709.13401.6109−1.61094.56700.10950.2841
Ibandronate → 2Mg2+−0.15010.17728.90620.3687−0.36874.45310.11230.0152
Ibandronate → 2Ca2+−0.12650.05855.0352−0.92520.92522.51760.19860.1700
Ibandronate → 2Sr2+−0.07930.14296.04800.8653−0.86533.02400.16530.1238
Neridronate → 2Mg2+−0.14680.16098.37260.1918−0.19184.18630.11940.0044
Neridronate → 2Ca2+−0.13640.04504.9377−1.24351.24352.46890.20250.3131
Neridronate → 2Sr2+−0.03280.18906.03572.1252−2.12523.01780.16570.7483
Pamidronate → 2Mg2+−0.10520.18077.78241.0272−1.02723.89120.12850.1356
Pamidronate → 2Ca2+−0.10420.08345.1081−0.28300.28302.55400.19570.0156
Pamidronate → 2Sr2+−0.05810.14585.54891.1932−1.19322.77440.18020.2566
∆E = ELUMO − EHOMO; µ = (EHOMO + ELUMO)/2; χ = −(EHOMO + ELUMO)/2; η = (ELUMO − EHOMO)/2; ζ = 1/(2η); ψ = µ2/(2η)
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Mollaamin, F.; Monajjemi, M. Carbon Nanotubes as Biosensors for Releasing Conjugated Bisphosphonates–Metal Ions in Bone Tissue: Targeted Drug Delivery through the DFT Method. C 2023, 9, 61. https://doi.org/10.3390/c9020061

AMA Style

Mollaamin F, Monajjemi M. Carbon Nanotubes as Biosensors for Releasing Conjugated Bisphosphonates–Metal Ions in Bone Tissue: Targeted Drug Delivery through the DFT Method. C. 2023; 9(2):61. https://doi.org/10.3390/c9020061

Chicago/Turabian Style

Mollaamin, Fatemeh, and Majid Monajjemi. 2023. "Carbon Nanotubes as Biosensors for Releasing Conjugated Bisphosphonates–Metal Ions in Bone Tissue: Targeted Drug Delivery through the DFT Method" C 9, no. 2: 61. https://doi.org/10.3390/c9020061

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