Assessing B₁₂N₁₂ and Al₁₂N₁₂ nanocages as potential vehicles for 1-(phthalazin-1(2H)-one)[(pyridin-2-yl)ethylidene]hydrazine, against onchocerciasis: a DFT study

Abstract

This work explores the potential of B₁₂N₁₂ and Al₁₂N₁₂ nanocages as carriers for 1-(phthalazin-1(2H)-one)[(pyridin-2-yl)ethylidene]hydrazone (APN). Density functional theory (DFT) calculations at M06/def2-SVP were conducted for energy minimization and at M06/def2-TZVP level for property calculations. Molecular electrostatic surface potential (ESP) analysis of APN identified two potential adsorption sites: the pyridine nitrogen (confA) and the azomethine nitrogen (confB). Thermochemical analysis indicates that the APN-nanocage complexes are energetically favorable, spontaneous and exothermic with confA complexes exhibiting the highest stability. Global reactivity studies indicate that complexation especially viaconfA significantly presents enhanced reactivity as evidenced by their lower HOMO–LUMO energy gaps and favourable electron transfer properties. QTAIM and NCI analyses show that the main interactions in the complexes are intermediate and non-covalent. Drug likeness analysis was equally performed and APN has a promising drug-like profile and could be a suitable candidate for further development as an orally bioavailable drug. Conclusively, both nanocages show promise as carriers for APN in the treatment of onchocerciasis.

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1. Introduction

Onchocerciasis (subcutaneous filariasis) arises from infection by the parasitic worm Onchocerca volvulus.^1,2 It is characterized by the presence of clinical manifestations such as cutaneous lesions and ocular manifestations known as river blindness.^1,2 Its transmission to humans occurs via the bites of the black fly (Simulium damnosum), a species known to breed in rapid-flowing bodies of water.^1,3,4 According to the 2015 WHO report, the African continent is the most vulnerable to river blindness and associated skin lesions, with an estimated incidence of approximately 35 million cases of Onchocerca volvulus infections.^5,6 Among the affected individuals, approximately 300 000 people are afflicted with blindness, while around 800 000 individuals experience varying degrees of visual impairment.^6,7 Onchocerciasis is ranked as the second most prevalent infectious cause of blindness after trachoma.⁵ Furthermore, this disease is linked to reduced life expectancy and elevated mortality rates among those infected, as well as social stigmatization of both affected individuals and their families.²

Due to the significant impact of onchocerciasis, various international organizations and donor groups have prioritized control measures for the disease.⁵ Over the last 40 years, extensive regional and local interventions have been implemented, particularly through the mass distribution of mectizan (ivermectin).^6,8 While these efforts have effectively controlled the disease, they have not yet led to its eradication.^5,9 Mectizan is highly effective against microfilariae but does not significantly affect macrofilariae.⁷ A yearly dose of mectizan over 15 to 18 years can potentially eliminate microfilariae in humans and interrupt transmission. However, this lengthy treatment regimen may lead to patient noncompliance and the risk of drug resistance. Recently, mectizan resistance has been observed in parasitic nematodes in veterinary contexts,⁹ raising concerns about its potential spread to the human strain, Onchocerca volvulus.⁸

These challenges highlight the urgent need for more effective anti-onchocercal drugs that can quickly target human Onchocerca volvulus. In response, several Schiff bases have been developed, including 1-(phthalazin-1(2H)-one)[(pyridin-2-yl)ethylidene]hydrazone (APN) (see Fig. 1), which has demonstrated significant micro- and macro-filaricidal activity, making it a promising candidate for anti-onchocercal treatment.⁷ Despite this, its delivery mechanism and efficacy require further exploration. The lack of targeted delivery systems hinders the potential therapeutic impact of these compounds, necessitating innovative approaches to enhance drug bioavailability and effectiveness. Moreover, this targeted delivery can easily be achieved by using nanomaterials such as boron nitride (B₁₂N₁₂) and aluminum nitride (Al₁₂N₁₂) nanocages. B₁₂N₁₂ is produced through an arc casting technique and identified via laser desorption TOF-MS.¹⁰B₁₂N₁₂ has gained significant attention in research due to its remarkable characteristics, including oxidation resistance and an appropriate energy gap for optoelectronic properties.¹¹ Due to its structural stability, it is commonly utilized in various forms, including nanoclusters,¹² nanotubes,^13,14 nanosheets^15,16 and nanocages.^11,17 Due to the structural and molecular similarities between boron and aluminum atoms,¹⁸ the Al₁₂N₁₂ nanocage has equally received attention. Additionally, both B₁₂N₁₂ and Al₁₂N₁₂ nanocages consist of 8 6-sided and 6 4-sided rings, which are reportedly more stable than their C₁₂N₁₂ and C₂₄ counterparts.^10,19 The polarity of the Al–N and B–N bonds in Al₁₂N₁₂ and B₁₂N₁₂, respectively, enhances the likelihood of biological molecules adsorbing onto their surfaces.

Fig. 1 Chemical structure of 1-(phthalazin-1(2H)-one)[(pyridin-2-yl)ethylidene]hydrazine (APN).

Although APN has exhibited notable micro- and macro-filaricidal activity against onchocerciasis, there has been no theoretical analysis of its interaction with B₁₂N₁₂ and Al₁₂N₁₂ nanocages as potential carrier molecules, warranting studies in this light. This study investigated the capability of B₁₂N₁₂ and Al₁₂N₁₂ nanocages as effective drug delivery systems for APNvia DFT. The choice of these nanomaterials is due to their biocompatibility and non-toxicity in biomedical, therapeutic, and diagnostic applications.^10,15 To evaluate the effectiveness of B₁₂N₁₂ and Al₁₂N₁₂ nanocages as delivery agents for APN, geometry optimization of APN and its complexes with both nanocages was performed, followed by thermochemical analysis. Furthermore, the electronic parameters of the molecules were evaluated, alongside the drug-likeness parameters of APN. DFT was employed as it provides a cost-effective and efficient approach and the fact that it accounts for electron correlation.²⁰ The findings from this theoretical investigation could pave the way for future experimental studies to validate the predicted interactions between APN and the selected nanocages.

2. Computational details

The quantum computations here utilized the ORCA version 5.0.3 tool.²¹ However, molecular orbitals for the molecular electrostatic surface potential (MESP) analysis were generated using ORCA version 3.0.1 (ref. 22) due to compatibility limitations with the visualization software. The MESP surfaces were visualized using Molekel 4.3,²³ which requires input files compatible only with earlier ORCA versions. To maintain consistency, single-point calculations in ORCA 3.0.1 were conducted at the same level of theory as those in ORCA 5.0.3. This approach ensured methodological uniformity while accommodating the technical requirements of the visualization tool. The input configurations were set up using Avogadro-1.1.1.²⁴ Geometry refinement then vibrational analyses were achieved through the M06 functional,²⁵ the def2-SVP basis set²⁶ and Grimme's D3 empirical dispersion correction. The M06 functional was selected based on its well-documented reliability in describing noncovalent interactions, thermochemistry and transition-metal bonding, which are critical features for accurately modelling nanocage–drug interactions. Specifically, M06 has demonstrated good performance in systems involving dispersion forces and charge transfer, as shown in previous benchmark studies.²⁷

The resolution-of-identity (RI-J)²⁸ and chain-of-spheres (COSX) approximations, collectively termed RIJCOSX, were utilized to greatly speed up the geometry refinement and vibrational analysis while maintaining a high level of accuracy with only a slight loss. Vibrational analyses reveal that all refined geometries align with stable structures, as shown by the lack of imaginary frequencies.

Based on the optimized structures, the adsorption energies (E_ads) for all configurations were calculated. E_ad was determined using the supramolecular method, consequently the related basis set superposition error (BSSE) was corrected by means of the geometrical counterpoise (gCP)²⁹ method. The gCP method was used as it provides BSSE corrections comparable in magnitude and accuracy to the full counterpoise approach.³⁰ The computed thermodynamic properties of the complexes comprised enthalpy change (ΔH_ad), entropy change (ΔS_ad) and Gibbs free energy change (ΔG_ad) at 1 atm and 298.15 K using Shermo-v2.6 utility software³¹ according to the following equations.

E_ad = E_APN/Cage − (E_cage + E_APN) + E_BSSE (1)

ΔH_ad = H_APN/Cage − (H_cage + H_APN) (2)

ΔS_ad = S_APN/Cage − (S_cage + S_APN) (3)

ΔG_ad = ΔH_ad − TΔS_ad (4)

here E, G, H and S denote the over-all electronic energy, Gibb's free energy, enthalpy and entropy, respectively. E_BSSE refers to the basis set superposition error.

To analyse APN's adsorption behaviour on B₁₂N₁₂ and Al₁₂N₁₂ nanocages, single-point energies (SPEs) were achieved via the M06/def2-TZVP computational approach. The M06 density functional was selected for its reliability in predicting molecular energies and accurately describing weak intermolecular forces, which are critical for modelling adsorption processes involving noncovalent interactions.^25,32 From the SPEs, the energy gap (E_g), chemical hardness (η), maximum transferred charge (ΔN_max), chemical potential (μ) and the electrophilicity (ω) were computed according to eqn (5)–(9):

E_g = E_LUMO − E_HOMO (5)

E_HOMO and E_LUMO signify the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies, respectively.

The non-covalent interaction (NCI) index and quantum theory of atoms-in-molecules (QTAIM) studies were executed with Multiwfn 3.8,³³ using molecular orbitals obtained from SPE calculations. These methods helped map out the weak intermolecular forces governing drug-nanocage binding interactions. To assess APN's suitability as a pharmaceutical candidate, we analyzed its absorption, distribution and safety profiles through SwissADME³⁴ and ADMETlab 3.0 (ref. 35) platforms.

3. Results and discussion

3.1 Optimized structures and molecular electrostatic surface potential (MESP) analysis

To identify favourable binding regions for APN on both nanocages the molecular electrostatic potential (ESP) surfaces were analysed. The MESP surface of APN (see Fig. 2) revealed two distinct nucleophilic sites primed for electrophilic interactions: pyridine nitrogen (site 1) and azomethine nitrogen (site 2). These electron-rich centres likely drive adsorption through electrostatic attraction to positively charged regions on the nanocage surfaces. The adsorption complexes formed at the two identified binding sites of APN were labelled as confA (site 1, pyridine nitrogen) and confB (site 2, azomethine nitrogen) to distinguish their structural configurations. Detailed geometric parameters, including refined Cartesian coordinates for all systems studied, are included in the ESI (see Tables S1–S7†).

Fig. 2 Molecular electrostatic surface potential (MESP) map of APN at M06/def2-SVP level.

The findings demonstrate that the optimal C=N bond lengths (B-Ls) at sites 1 and 2 in APN are determined to be 1.327 Å and 1.292 Å, respectively. Upon adsorption of APN onto the B₁₂N₁₂ surface, these B-Ls increase to 1.345 Å (in confA) and 1.303 Å (in confB). The observed elongation in bond lengths indicates stronger APN/nanocages interactions. For example, the B–N bond in the pristine B₁₂N₁₂ nanocage stretches from 1.435 Å to 1.570 Å in confA and 1.531 Å in confB. Similarly, the Al–N bond in the pristine Al₁₂N₁₂ nanocage extends from 1.843 Å to 1.860 Å in confA and 1.873 Å in confB after APN adsorption. These changes in B-Ls point to structural distortions in the nanocages, likely caused by the adsorption process. The expansion of these bonds highlights the significant influence of APN on the nanocage geometry, reflecting the strength of the interactions at play. These structural changes are consistent with those reported elsewhere,³⁶ further supporting the potential adsorption of APN on the nanocages under investigation.

Typically, bond lengths falling within the range of 1.0–3.5 Å are indicative of chemisorption, whereas those exceeding 3.5 Å usually point to physisorption.³⁷ In this study, the APN–B₁₂N₁₂ B-Ls are measured at 1.657 Å (in confA) and 1.662 Å (in confB), as depicted in Fig. 3. Furthermore, the APN–Al₁₂N₁₂ B-Ls are recorded to be 2.055 Å and 2.066 Å in confA and 2.088 Å and 2.261 Å in confB. These findings imply that the interaction between APN and both nanocages can be classified as chemisorption, with that of the B₁₂N₁₂ nanocage being stronger.

Fig. 3 Optimized structures APN and its complexes with B₁₂N₁₂ and Al₁₂N₁₂.

3.2 Thermodynamic properties

Summarised in Table 1 are the values of the thermodynamic properties computed in this study.

Table 1 Entropic term (TS), adsorption energy (E_ad), enthalpy changes (ΔH_ad), entropic variations (TΔS_ad) at 298.15 K and Gibb's free energy changes (ΔG_ad) of the studied compounds (all values are in kcal mol⁻¹) at M06/def2-TZVP level of theory

Molecule	TS	E ad	ΔHad	TΔSad	ΔGad
APN	37.19	—	—	—	—
B12N12	27.26	—	—	—	—
APN–B12N12confA	49.88	−57.90	−29.81	−14.56	−15.25
APN–B12N12confB	50.46	−43.24	−26.81	−13.99	−12.82
Al12N12	39.39	—	—	—	—
APN–Al12N12confA	60.18	−34.99	−55.14	−16.40	−38.73
APN–Al12N12confB	60.41	−31.55	−42.12	−16.17	−25.95

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The calculated E_ads are consistently negative, confirming that the formation of APN/Al₁₂N₁₂ and APN/Al₁₂N₁₂ complexes are energetically favourable. It can equally be observed from the data in the table that the E_ads of complexes formed with B₁₂N₁₂ are higher (about 23 times for confA and about 11 times for confB) than those formed by Al₁₂N₁₂. This implies that confA forms the most stable adsorption complexes. The E_ads values range from −65.12 to −31.55 kcal mol⁻¹, which falls within the range typically associated with chemisorption. This aligns with the formation of strong chemical bonds between APN and the nanocage surfaces, further supporting the stability and strength of the interactions.

Additionally, the negative ΔH_ads values confirm the exothermic nature of the adsorption processes, indicating that the formation of the APN-nanocage complexes is associated with energy-releasing stabilizing interactions. Furthermore, the computed ΔG_ads are all negative (−55.19 to −12.82 kcal mol⁻¹), demonstrating that the adsorption of APN onto the nanocages is a spontaneous process.

3.3 Topological analysis

To better understand the stability and type of the APN/nanocages interactions, Bader's Quantum Theory of Atoms in Molecules (QTAIM)³⁸ was applied. It analyzes key metrics at the bond critical points (BCPs), including the total electron density (ρ(r)), its Laplacian (∇²ρ(r)) and the energy densities (H(r), V(r) and G(r)). According to QTAIM, specific parameter ranges correspond to different interaction types: non-covalent interactions ∇²ρ(r) > 0 a.u., H(r) > 0 a.u., and |V(r)|/G(r) < 1; intermediate interactions (e.g., partial covalent bonds, coordination bonds): H(r) < 0 a.u., ∇²ρ(r) > 0 a.u., and 1 < |V(r)|/G(r) < 2 and covalent bonds: H(r) ≪ 0 a.u., ∇²ρ(r) < 0 a.u., and |V(r)|/G(r) > 2. The evaluated QTAIM parameters for the APN-nanocage bonds are summarized in Table 2.

Table 2 Topological metrics at BCPs APN-nanocage bonds in the complexes studied, (all in a.u.), at M06/def2-TZVP level of theory

Complex	APN–B12N12				APN–Al12N12
	ConfA		ConfB		ConfA		ConfB
Bond	B–N	N–H	B–N	N–H	Al–N	N–H	Al–N	N–H
ρ(r)	0.116	0.019	0.117	0.369	0.053	0.021	0.050	0.027
∇^2ρ(r)	0.141	0.059	0.123	1.079	0.234	0.075	0.210	0.088
H(r)	−0.097	0.002	−0.098	0.608	−0.004	0.002	−0.004	0.001
G(r)	0.132	0.013	0.129	0.339	0.062	0.017	0.056	0.021
V(r)	−0.228	−0.012	−0.227	−0.947	−0.066	−0.015	−0.061	−0.020
|V(r)|/G(r)	1.733	−0.878	1.761	−2.797	1.059	−0.889	1.072	−0.946

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Table 2 reveals that for all adsorbate–adsorbent interactions occurring through B–N and Al–N bonds at sites 1 and 2, the QTAIM parameters satisfy the conditions H(r) < 0 a.u., ∇²ρ(r) > 0 a.u., and 1 < |V(r)|/G(r) < 2, confirming that these interactions are partially covalent. The magnitudes of these topological parameters reveal that the bonds in the APN–B₁₂N₁₂ complexes exhibit significantly stronger covalent character compared to those in the APN–Al₁₂N₁₂ complexes. These findings suggest that APN can be easily physisorbed or chemisorbed onto the B₁₂N₁₂ nanocage, while it is primarily physisorbed on the Al₁₂N₁₂ nanocage. In contrast, interactions formed via N–H bonds at the same sites exhibit ∇²ρ(r) > 0 a.u., H(r) > 0 a.u., and |V(r)|/G(r) < 1, indicating the presence of non-covalent interactions. These outcomes are in line with the molecular graphs (see Fig. 4), which visually depict the bonding patterns between APN/nanocages.

Fig. 4 Molecular graphs characterizing the BCPs of the APN/nanocages interactions.

The molecular graphs reveal that APN's adsorption is stabilized not only by B–N and Al–N bonds but also through non-covalent interactions. These additional connections contribute to the overall stability of the APN/nanocage complexes, further supporting the robustness of the adsorption process.

3.4 Non-covalent interaction (NCI) index analysis

The non-covalent interaction (NCI) index scheme is a powerful tool employed to identify and visualize weak interactions in the APN-nanocage complexes. It is based on the reduced density gradient (RDG), which is calculated from the electron density (ρ(r)) and its first derivative (∇ρ(r)). The RDG-based analysis excels at mapping out weak interactions, such as hydrogen bonds and van der Waals forces and can be seen as a complementary extension of QTAIM theory, offering a more visual and intuitive understanding of these interactions.³⁹

In NCI framework, the nature and strength of weak interactions are determined by analysing the product of the Hessian matrix's sign(λ₂) and ρ(r). This approach is typically visualized using RDG vs. sign(λ₂)ρ(r) plots, which pinpoint specific regions of non-covalent interactions on the molecular surface. The following colour code is used to identify weak interaction types: blue (sign(λ₂)ρ(r) < 0) for attractive interactions (covalent and hydrogen bonding), green (sign(λ₂)ρ(r) ≈ 0) for van der Waals and dispersive interactions and red (sign(λ₂)ρ(r) > 0) for repulsive interactions, such as steric clashes.^39,40Fig. 5 presents both 2D and 3D RDG plots, offering a detailed visualization of the interactions between APN and the nanocages.

Fig. 5 Panels (a), (b), (e) and (f) display 2D RDG vs. sign(λ₂)ρ(r) plots; panels (c), (d), (g) and (h) show 3D RDG isosurfaces, generated with Multiwfn 3.8 using a RDG (s(r)) of 0.05 a.u. and visualized in VMD 1.9. The isosurfaces are color-coded on a red-yellow-green-blue scale with sign(λ₂)ρ(r) values spanning −0.05 to 0.05 a.u.

The RDG plots exhibit distinct spikes corresponding to sign(λ₂)ρ(r) values in the −0.01 to 0.01 a.u. interval, which indicates the existence of weak dispersive interactions, primarily between APN and the nanocage surfaces. Spikes at sign(λ₂)ρ(r) ≈ −0.02 a.u. point to strong hydrogen bonding and partially covalent interactions, consistent with the findings from the QTAIM analysis. Furthermore, spikes at sign(λ₂)ρ(r) > 0.02 a.u. highlight steric clashes, particularly within the aromatic rings of APN. The NCI and QTAIM analyses are in strong agreement, confirming that intermediate and non-covalent interactions play a key role in stabilizing the adsorption of APN on the outer surfaces of both nanocages.

3.5 Global reactivity descriptors (GRDs)

To shed some light on the reactivity of the investigated molecules, their conceptual DFT-based GRDs were computed at M06/def2-TZVP theoretical level and values enumerated in Table 3.

Table 3 HOMO energy (E_HOMO), LUMO energy (E_LUMO), chemical potential (μ), HOMO–LUMO energy gap (E_gap), electrophilicity (ω), chemical hardness (η), and electron transfer index (ΔN_max) (in eV)

Molecule	E HOMO	E LUMO	E gap	μ	η	ω	ΔNmax
APN	−5.887	−1.794	4.093	−3.841	2.047	3.604	1.877
B12N12	−8.364	−0.872	7.492	−4.618	3.746	2.846	1.233
APN–B12N12confA	−6.209	−2.453	3.756	−4.331	1.878	4.994	2.306
APN–B12N12confB	−6.706	−2.272	4.434	−4.489	2.217	4.545	2.025
Al12N12	−6.877	−2.205	4.672	−4.541	2.336	4.414	1.944
APN–Al12N12confA	−5.877	−2.353	3.524	−4.115	1.762	4.805	2.335
APN–Al12N12confB	−6.028	−2.277	3.751	−4.153	1.876	4.597	2.214

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Molecules with small HOMO–LUMO energy gaps can transition from ground → excited state with relatively low energy input. In contrast, those with large HOMO–LUMO gaps demand significantly more energy for the same transition.⁴¹ The results show that confA (with E_gap = 3.56 eV) and confB (with E_gap = 4.434 eV) comprising the B₁₂N₁₂ nanocage have lower energy gaps than the monomers APN (with E_gap = 4.093 eV) and B₁₂N₁₂ (with E_gap = 7.492 eV). A similar pattern can be seen for pristine Al₁₂N₁₂ nanocage and its complexes. Therefore, adsorption of APN onto the surfaces B₁₂N₁₂ and Al₁₂N₁₂ increases its reactivity thereby making it more suitable for applications in biological systems.

Chemical potential (μ) reflects how readily a system can exchange electron density with its surroundings, while chemical hardness (η) quantifies a molecule's resistance to such exchange.⁴² Generally, molecules with low η and high μ exhibit greater reactivity but lower stability within a chemical system, as they are more prone to participate in electron transfer processes. On this basis, APN–B₁₂N₁₂confA (with μ = −4.331 and η = 1.878) is more reactive and less stable than APN–B₁₂N₁₂confB (with μ = −4.489 and η = 2.217). A similar pattern is observed for the Al₁₂N₁₂ nanocage with μ = −4.115 and η = 1.762 for confA and μ = −4.153 and η = 1.876 for confB.

In many cases of molecular reactivity, electron density transfer from a donor to an acceptor species occurs.⁴² Molecules with highly positive values of electrophilicity ω and electron transfer index ΔN_max have a greater tendency to accept electron density. Data from the table depict that both APN–B₁₂N₁₂confA (with ω = 4.994 eV and ΔN_max = 2.306 eV) and of APN–Al₁₂N₁₂confA (with ω = 4.805 eV and ΔN_max = 2.336 eV) are better electrophiles than of APN–B₁₂N₁₂confB (with ω = 4.545 eV and ΔN_max = 2.025 eV) and of APN–Al₁₂N₁₂confB (with ω = 4.597 eV and ΔN_max = 2.214 eV). Conclusively, the GRDs suggest that confA of both APN–B₁₂N₁₂ and APN–Al₁₂N₁₂ are the most are most suitable for biological applications.

3.6 Recovery time

Recovery time (τ) is a key parameter that indicates how swiftly a drug molecule detaches from its carrier,^43,44 making it vital for effective drug delivery mechanisms.⁴⁵ Complexes with high adsorption energies tend to be more stable, but they may face challenges in releasing the drug efficiently in biological surroundings.⁴³ Consequently, a shorter recovery time signifies a faster desorption rate, which enhances the drug's therapeutic effectiveness. In this study, τ was calculated using eqn (11) at room temperature, and the results are presented in Table 4.where, V_o: attempt frequency (10¹² s⁻¹), E_ad: the absolute value of adsorption energy, T: temperature at 298.15 K and K: Boltzmann constant, 2 × 10⁻³ kcal mol⁻¹ K⁻¹.

Table 4 Computed recovery time of the studied complexes (in second (s))

Complex	Recovery time (τ) in s
APN–B12N12confA	3.26 × 10^−36
APN–B12N12confB	1.05 × 10^−33
APN–Al12N12confA	6.681 × 10^−53
APN–Al12N12confB	3.23 × 10^−42

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For each nanocage examined, confA exhibits a shorter τ than confB. For example, τ for APN–B₁₂N₁₂confA is approximately 322 times lower than that of confB. Likewise, τ for the APN–Al₁₂N₁₂confA is several hundred times shorter compared to its confB counterpart. This indicates that APN can be readily desorbed from the confA's of its complexes with both APN–B₁₂N₁₂ and APN–Al₁₂N₁₂ nanocarriers. These rapid recovery times suggest that despite strong binding, APN can be efficiently released from both nanocarriers, with B₁₂N₁₂ offering a favorable balance between stability and controlled release.

3.7 Drug-likeness analysis of APN

A drug-like molecule is characterized by possessing acceptable pharmacokinetic and physicochemical parameters.^46,47 Key pharmacokinetic parameters that influence in vivo drug activity include systemic exposure, which covers the procedures of absorption, distribution, metabolism, and excretion (ADME); bioavailability, which reflects the extent and rate of drug absorption and metabolism; and elimination, which is determined by the interplay of metabolism, distribution and excretion.⁴⁷ To assess the crucial physicochemical properties of APN, analyses were performed using the SwissADME.³⁴ and ADMETlab 3.0.³⁵ web servers, as detailed in Table 5.

Table 5 SWISSAMDE and ADMETlab 3.0 predicted drug-likeness parameters

Parameters	SwissADME	ADMETlab 3.0
M W (g mol^−1)	263.3	263.12
nRB	2	2
nHBA	4	5
nHBD	1	1
TPSA Å^2	66.29	66.29
LogP	2.47	2.96
LogS (ESOL)	−3.26	—
Ali LogS (Ali)	−3.12	—
LogS (Silicos-IT)	−6.01	—
Lipinski violation	0	Accepted (0)
Veber violation	0	—

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Table 5 includes experimental data alongside predictions derived from Lipinski's Rule of Five (LOF),⁴⁸ a widely used guideline for assessing oral drug absorption. According to this rule, compounds are more probable to display poor oral bioavailability if they fail to meet 2 or extra of the subsequent criteria: molecular weight (MW) ≤ 500 Da; octanol–water partition coefficient (LogP) < 5; hydrogen bond acceptors (nHBA) ≤ 10; hydrogen bond donors (nHBD) ≤ 5.⁴⁸ Veber's criteria⁴⁹ complement these guidelines by focusing on molecular flexibility and polarity: rotatable bonds (nRB) ≤ 10; topological polar surface area (TPSA) ≤ 140 Ų (indicating better cell permeability).

The results obtained from SwissADME and ADMETlab 3.0 are similar and show no violations to LOF. This compliance with the Lipinski rule demonstrates good oral bioavailability of APN. Moreover, the results are also in conformity with the Veber's rule, further confirming its high cell membrane permeability. APN's aqueous solubility was assessed using three SwissADME models: ESOL, Ali and Silicos-IT. The ESOL model predicted a solubility (LogS) of −3.26, and the Ali model predicted a LogS of −3.12, both indicating moderate solubility, which supports the compound's potential for oral administration without major formulation challenges. In contrast, the Silicos-IT model predicted a much lower LogS of −6.01, classifying the compound as poorly soluble. This discrepancy likely reflects the model's sensitivity to molecular flexibility and hydrophobicity. While ESOL and Ali suggest favorable solubility for drug development, the Silicos-IT result highlights the need for caution in formulations where high aqueous solubility is critical. These findings suggest a high probability of oral bioavailability, particularly strong oral absorption and efficient gastrointestinal permeability. The physicochemical properties of APN align well with the requirements for achieving favourable pharmacokinetic behaviour in the human body, ensuring they can effectively reach systemic circulation and exert their therapeutic effects.

In addition to physicochemical properties, ADMET-related properties⁵⁰ comprising Human Intestinal Absorption (HIA), Caco-2 cell membrane permeability, Madin–Darby Canine Kidney (MDCK) cell membrane permeability, bioavailability (F20% and F30%), Blood–Brain Barrier (BBB) penetration, Volume of Distribution at Steady State (VDss), Plasma Protein Binding (PPB), Fraction Unbound (Fu) in plasma, P-glycoprotein (P-gp) substrates and inhibitors, cytochrome P450 substrates and inhibitors, Drug-Induced Liver Injury (DILI), Human Hepatotoxicity (H-HT), Human Ether-a-Go-Go-Related Gene (hERG) inhibition, AMES toxicity, were evaluated to assess the drug's behaviour in biological systems and their values summarized in Table 6.

Table 6 ADMET-related metrics for APN, predicted by ADMETLab 3.0^a

Properties	Score/result
a The prediction probability values are represented using the following: −: 0–0.1; −−: 0.1–0.3; −−−: 0.3–0.5; +: 0.5–0.7; ++: 0.7–0.9; +++: 0.9–1.0. Interpretation: +++ or ++ suggests a higher likelihood of toxicity or defectiveness; −−− or −− indicates a non-toxic or appropriate molecule and + or – represents inconclusive results, requiring further evaluation.
Adsorption
Caco-2 permeability (log unit)	−4.506
MDCK permeability (cm s^−1)	−4.572
P-gp inhibitor	+
P-gp substrate	−−−
HIA	−−−
F20%	−−−
F30%	−−−
Distribution
PPB	95.7%
VDss	0.294
BBB penetration	−−−
Fu	4.1%
Metabolism
CYP1A2 inhibitor	+++
CYP1A2 substrate	++
CYP2C19 inhibitor	++
CYP2C19 substrate	−−−
CYP2C9 inhibitor	++
CYP2C9 substrate	−−
CYP2D6 inhibitor	−−−
CYP2D6 substrate	−−−
CYP3A4 inhibitor	+
CYP3A4 substrate	−−−
CYP2B6 inhibitor	−−−
CYP2B6 substrate	−−−
CYP2C8 inhibitor	+++
HLM stability	++
Excretion
Clearance (Ml min^−1 kg^−1)	2.819
Half-life (h)	0.929
Toxicity
hERG blockers	−
DILI	+++
AMES toxicity	+
Human Hepatotoxicity (H-HT)	++
Skin sensitization	+++
Carcinogenicity	+
Eye corrosion	−
Eye irritation	+++
Respiratory toxicity	+++

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Table 6 highlights that APN demonstrates favourable intestinal absorption and permeability. It exhibits high Caco-2 cell permeability (−4.506 log unit) and moderate MDCK cell permeability (−4.572 cm s⁻¹), indicating that its absorption in the intestines likely occurs via passive transcellular transport crosswise the epithelial lining, as further supported by HIA data. APN is also identified as a potential P-gp substrate, an efflux transporter that could enhance its bioavailability, as suggested by F20% and F30% values. However, its potential to inhibit P-gp remains unclear, which could lead to interactions with other P-gp-transported drugs, potentially slowing their absorption. Regarding drug distribution, APN shows high plasma protein binding (PPB > 90%), which may limit its access to therapeutic targets. Nevertheless, its predicted volume of distribution (VDss) falls within the optimal 0.04–20 l kg⁻¹ interval, indicating substantial tissue distribution rather than concentration in plasma. The low fraction unbound (Fu < 5%) suggests that a smaller proportion of APN remains free in plasma, allowing it to diffuse across cell membranes into tissues, a finding supported by its high blood–brain barrier (BBB) penetration. From an excretion perspective, APN has a low clearance rate (∼2.82 ml min⁻¹ kg⁻¹) but a short elimination half-life (∼0.9 hours), reducing the likelihood of significant accretion in the body. In silico metabolism profiling indicates that APN interacts with multiple cytochrome P450 (CYP) enzymes. It is predicted to be a strong inhibitor of CYP1A2 and CYP2C8, and a moderate inhibitor of CYP2C19, CYP2C9 and CYP3A4. These interactions suggest a high potential for drug–drug interactions, particularly when co-administered with drugs that are metabolized by these enzymes. In terms of substrate liability, APN is predicted to be a substrate of CYP1A2, but not of CYP2C9, CYP2C19, CYP2D6, CYP2B6 or CYP3A4, indicating a limited chances of APN metabolism by these enzymes. Despite the weak CYP3A4 inhibition, the absence of CYP3A4 substrate behaviour may reduce the risk of rapid hepatic clearance. APN demonstrates moderate human liver microsomal (HLM) stability, suggesting that it is not rapidly metabolized and may exhibit favourable hepatic metabolic stability. However, the predicted multi-CYP inhibition, especially of CYP1A2 and CYP2C8, highlights the need for further in vitro metabolic profiling of APN.

Based on the predicted toxicological parameters, APN may pose an elevated risk of respiratory toxicity, skin sensitization, eye irritation, and liver injury. It also exhibits moderate human hepatotoxicity but shows low risks of carcinogenicity, hERG inhibition, eye corrosion, and AMES toxicity. These findings suggest that APN is a safe molecule for use in the subcutaneous treatment of filariasis (onchocerciasis).

4. Conclusion

This research explores the likelihood of B₁₂N₁₂ and Al₁₂N₁₂ nanocages as drug delivery systems for the anti-onchocercal compound 1-(phthalazin-1(2H)-one)[(pyridin-2-yl)ethylidene]hydrazone (APN). DFT calculations were conducted at the M06/def2-SVP and M06/def2-TZVP levels for energy minimization and property calculations, respectively. Molecular Electrostatic Potential (MESP) analysis identified two potential adsorption sites on APN: the pyridine nitrogen (confA) and the azomethine nitrogen (confB). Thermochemical analysis confirmed that the formation of APN-nanocage complexes is energetically favourable, exothermic and spontaneous, with confA complexes demonstrating the highest stability. Global reactivity studies indicate that complexation, particularly viaconfA, significantly enhances reactivity, as evidenced by lower HOMO–LUMO energy gaps and favourable electron transfer properties. QTAIM and NCI analyses revealed that the primary interactions in the complexes are intermediate and non-covalent. APN exhibits a promising drug-like profile, making it a strong candidate for further development as an orally bioavailable drug. The findings demonstrate that B₁₂N₁₂ and Al₁₂N₁₂ nanocages have significant potential as effective drug transport systems for APN in the treatment of onchocerciasis.

Data availability

The data that support the findings of this study are included in the ESI† of this article.

Conflicts of interest

The authors declare no conflicts of interest regarding the publication of this paper.

Acknowledgements

The authors are thankful to the Ministry of Higher Education of Cameroon for their support to University Lecturers.

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Footnote

† Electronic supplementary information (ESI) available: Additional tables constituting part of this work. Tables S1–S7 gives the optimized geometrical coordinates. See DOI: https://doi.org/10.1039/d5na00360a

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