Mechanistic and energetic studies of superparamagnetic iron oxide nanoparticles as a cyclophosphamide anticancer drug nanocarrier: A quantum mechanical approach

Abstract

Using Fe₆(OH)₁₈(H₂O)₆ as a ring cluster model for superparamagnetic iron oxide nanoparticles, noncovalent configurations and three mechanisms of covalent functionalization of superparamagnetic iron oxide nanoparticles with cyclophosphamide an anticancer drug were studied. Quantum molecular descriptors, solvation, and binding energies of noncovalent interactions were investigated the in gas and solution phases at the B3LYP and M06-2X density functional levels. In the vicinity of superparamagnetic iron oxide nanoparticles, the reactivity of the drug increases, showing cyclophosphamide can probably bind to superparamagnetic iron oxide nanoparticles through Cl (k₁ mechanism), P=O (k₂ mechanism), and NH in a six-membered ring (k₃ mechanism) groups. The activation parameters of all pathways were calculated, indicating the high barriers related to the k₁ and k₂ mechanisms are higher the barrier related to the k₃ mechanism. The k₃ mechanism is also spontaneous and exothermic and is therefore the preferred mechanism for covalent functionalization.

Introduction

Superparamagnetic iron oxide nanoparticles (SNPs) consist of elements such as iron, cobalt, nickel, and their oxides which are increasingly utilized in different areas.^1–4 Due to their unique chemical and electronic properties, these materials are employed in biological and pharmaceutical research.^5–9 SNPs have a large surface-to-volume ratio, and for this reason, they could be used effectively to transfer different materials including therapeutic agents.^10–16

The use of magnetism in medicine was introduced by Freeman et al. in the 1970s. ¹⁷ Since that time, much research has been done in this field, which has led to the design of different magnetic particles. Generally, drugs do produce some side effects, which normally arise from lack of precision and specificity in drug action. Targeted drug delivery for diseases such as cancer causes lower dosage of drugs to be required, consequently leading to reduction of side effects such as vomiting, breathing trouble, cardiotoxicity, and hair loss.^18,19

The magnetic properties of SNPs make them suitable to be guided towards the intended site such as a cancerous tumor by an external magnetic field.^5,20,21 The drug will be released in cancer tissues by factors such as enzymatic activity, changes in pH, temperature, and osmolality.^22,23

Iron oxide can exist as different chemical compositions, such as magnetite (Fe₃O₄) and maghemite (γ-Fe₂O₃). These particles demonstrate the phenomenon of superparamagnetism. ²⁴ SNPs are small synthetic Fe₃O₄ (magnetite), γ-Fe₂O₃ (maghemite), or α-Fe₂O₃ (hematite) particles.^25,26 In the presence of an external magnetic field, SNPs become magnetized up to their saturation magnetization and, in the absence of an external magnetic field, they do not show any residual magnetic interaction. This property is dependent upon size, and generally increases when the diameter of the iron oxide nanoparticles is as low as 10–20 nm. Magnetite and maghemite have the widest usage in biomedical applications. Covalent and noncovalent (hydrogen bonds and van der Waals interactions) functionalizations^25,27–30 play a principal role in drug delivery and biological applications using iron oxide nanoparticles. The possibility of targeted drug delivery causes reduction of the amount of drugs consumed and consequently the reduction of their side effects.^31–33 This superparamagnetism, exclusive to nanoparticles, is very valuable for their application as a drug delivery vehicle because they can actually drag drug molecules to their target site in the body under the impact of an external magnetic field.^34–36

Cyclophosphamide (CP) or cytophosphane, has anticancer activities and is effective in the treatment of lymphoma, leukemia, multiple myeloma, ovarian cancer, breast cancer, sarcoma, neuroblastoma, and small-cell lung cancer.^37,38 The formulation of appropriate molecular models in solution (especially water) is of special importance in understanding the mechanistic behavior of drug delivery systems such as SNPs.

The most appropriate method for designing such models is quantum chemical calculations. In 2016, the chemistry Nobel Prize was awarded for the design and manufacture of molecular machines, an important application of which is in drug delivery systems.^39–41

In this work, we have used quantum chemical calculations to analyze mechanisms of noncovalent and covalent functionalization^42,43 of SNPs with cyclophosphamide drug needed. So far, little research has been done on the mechanism of functionalization of SNPs, and therefore, this work could inspire researchers in the design and manufacture of new drug delivery systems.

Computational method

All quantum chemical calculations have been done using the GAUSSIAN 09 package ⁴⁴ at the B3LYP^45–47 hybrid density functional level together with the 6-31G(d,p) basis set.^48,49 For Fe atoms, the LANL2DZ basis set ⁵⁰ with effective core potential functions was employed. We repeated the calculations for noncovalent functionalization using the M06-2X functional^51,52 which implicitly accounts for “medium-range” electron correlation (systems separated by about 5 Å or less), ⁵³ as M06-2X can describe the dispersion interactions within many systems. ⁵⁴ Standard convergence criteria for geometry optimization were used. For all configurations, all degrees of freedom were optimized. The transition states obtained were confirmed to have only one imaginary frequency of the Hessian. The zero-point corrections were also used to calculate activation energies. To achieve higher accuracy, approximation methods such as ONIOM ⁵⁵ were not used.

The solvent can have a significant effect on chemical systems and reactions explicitly^56–61 or implicitly. The polarized continuum model (PCM) method was used to consider the implicit role of the solvent.^62,63 Using the Solvation Model based on Density (SMD) solvation model, ⁶⁴ the effect of solvation has also been calculated. In this model, the free energy of solvation is evaluated using the following equation

$$\Delta G_{\mathrm{solv}}=(E_{\mathrm{solv}}+\Delta G_{\mathrm{nonelectrostatic}})-E_{\mathrm{gas}}$$

(1)

where E_solv and E_gas represent the total energies of the system in the solution phase and gas phase, respectively, and $\Delta G_{\mathrm{nonelectrostatic}}$ is the nonelectrostatic energy.

For the description of chemical reactivity and stability, quantum molecular descriptors such as hardness and electrophilicity index were used. The global hardness $(\eta )$ indicates the resistance of one molecule against change in its electronic structure (equation (2))

$$\eta =\frac{(I-A)}{2}$$

(2)

where $I=-E_{\mathrm{HOMO}}$ and $A=-E_{\mathrm{LUMO}}$ (highest occupied molecular orbital (HOMO)and lowest unoccupied molecular orbital (LUMO)) are the ionization potential and the electron affinity of the molecule, respectively.

Parr defined the electrophilicity index $(\omega )$ as follows ⁶⁵

$$\omega =\frac{{\mu }^2}{2\eta }$$

(3)

Results and discussion

CP contains functional groups such as Cl, NH, and PO and has a nonplanar structure as shown in Figure 1. SNPs were modeled using γ-Fe₂O₃ nanoparticles in the solution phase (clusters of Fe₆(OH)₁₈(H₂O)₆ rings, including six-edge sharing octahedra joined via 12 OH groups and 6 surface OH and H₂O ⁶⁶ groups). The optimized geometries of the SNP γ-Fe₂O₃ and CP in the solution phase (water) are shown in Figure 1. Different configurations, during which the CP drug approaches the SNP via Cl, PO, and NH groups were called SNP/CP1, SNP/CP2, and SNP/CP3, respectively. For PO and NH groups, one structure was obtained (SNP/CP2,3). These reactants form hydrogen and pseudo-hydrogen bonds (Figure 2).

Figure 1.

Optimized structures of SNP and CP.

Figure 2.

Optimized structures of SNP/CP1 and SNP/CP2,3.

The free energies of solvation $(\Delta G_{\mathrm{solv}})$ were calculated using the SMD solvation model. The solvation energies of CP, SNP, and SNP/CP1-2,3 are shown in Table 1. The calculated solvation energies show that CP solubility increases in the presence of the SNP. For the SNP/CP2,3 configuration, functionalization of the SNP with CP causes an increase in the solubility of the SNP which is an important factor for its applicability in drug delivery. The important characteristic of CP is in having NH and PO functional groups, causing strong hydrogen bonding between the drug and SNP, which is the reason that this drug is a suitable candidate for delivery by SNPs.

Table 1.

Solvation and binding energies of different configurations (kJ mol⁻¹).

Species	$\Delta G_{\mathrm{solv}}$	$\Delta E_{\mathrm{B}3\mathrm{LYP}}$	$\Delta E_{\mathrm{B}3\mathrm{LYP}}$	$\Delta E_{\mathrm{M}06-2\mathrm{X}}$	$\Delta E_{\mathrm{M}06-2\mathrm{X}}$
CP	−46.77	Solution phase	Gas phase	Solution phase	Gas phase
SNP	−126.25
SNP/CP1	−116.55	29.43	−27.05	4.56	−53.48
SNP/CP2,3	−141.12	−9.62	−41.52	−35.23	−67.26

CP: cyclophosphamide; SNPs: superparamagnetic iron oxide nanoparticles.

The binding energies $(\Delta E)$ of CP to the SNP in the gas and solution phases were calculated using the following equation and are presented in Table 1

$$\Delta E=E_{\mathrm{SNP}/\mathrm{CP}1-2,3}-(E_{\mathrm{SNP}}+E_{\mathrm{CP}})$$

(4)

The calculated binding energies of SNP/CP2,3 are negative in both gas and solution phases. SNP/CP2,3 is more stable than SNP/CP1 in both phases. We repeated the calculations using the M06-2X functional to consider the contribution of dispersion interactions. The calculated binding energies related to M06-2X are more negative than those related to B3LYP (Table 1). Comparison between SNP/CP2,3 and SNP/CP1 shows that the former is more stable due to the stronger hydrogen bond between CP and SNP.

Quantum molecular descriptors for CP, SNP, and SNP/CP1-2,3 in both phases are represented in Table 2. In Table 2, E_g is the energy gap between LUMO and HOMO. Table 2 shows that the calculated values of η and E_g related to CP are remarkably more than those of SNP/CP1-2,3, meaning that the reactivity of the drug increases in the vicinity of the SNP. Also, ω for CP increases in the presence of the SNP, showing that CP acts as an electron acceptor.

Table 2.

Quantum molecular descriptors (eV) and binding energies (kJ mol⁻¹) of CP, SNP, and SNP/CP1-2,3.

Species	E HOMO	E LUMO	E g	$\eta$	$\omega$
	Solution phase (water)
CP	−6.80	0.17	6.98	3.49	1.58
SNP	−5.58	−4.48	1.10	0.55	22.95
SNP/CP1	−5.56	−4.46	1.10	0.55	22.77
SNP/CP2,3	−5.49	−4.44	1.05	0.52	23.52
	Gas phase
CP	−6.85	0.20	7.05	3.53	1.56
SNP	−5.41	−4.36	1.05	0.53	22.68
SNP/CP1	−5.58	−4.30	1.28	0.64	19.12
SNP/CP2,3	−5.35	−4.27	1.07	0.54	21.59

CP: cyclophosphamide; SNPs: superparamagnetic iron oxide nanoparticles.

In order to study the possibility of formation of a covalent bond^67,68 between the SNP and CP, we considered three mechanisms. First, we selected SNP/CP3 for the verification of covalent functionalization in the solution phase. In this case, NH in SNP/CP3 attacks the Fe atom to transfer its proton to the surface OH group of the SNP (Scheme 1). In this mechanism, reactant SNP/CP3 loses an H₂O molecule to give product SNPCP3/H₂O. The optimized structure of product SNPCP3/H₂O is shown in Figure 3.

Scheme 1.

Mechanism k₃.

Figure 3.

Optimized structure of SNPCP3/H₂O.

The transition state of step k₃ (TS _{k 3} ) was obtained through reactant SNP/CP2,3 and product SNPCP3/H₂O and is presented in Figure 4. The calculated bond lengths for this mechanism are shown in Figures 2 –4.

Figure 4.

Optimized structure of TS _{k 3} .

If the electronic plus zero-point energy (E), enthalpy (H), and Gibbs free energy (G) of SNP + CP become equal to zero, then the relative energies of the optimized structures in all pathways will be obtained. The total activation energy $E_{\mathrm{a}}$ , activation enthalpy $(\Delta H^{‡})$ , and activation Gibbs free energy $(\Delta G^{‡})$ for mechanism k₃ are 44.48, 47.54, and 65.67 kJ mol⁻¹, respectively (Table 3).

Table 3.

Relative energies (kJ mol⁻¹) for different species in mechanisms k₁–k₃.

Species	$\Delta E$	$\Delta H$	$\Delta G$
	Mechanism k1
SNP + CP1	0.00	0.00	0.00
SNP/CP1	29.43	31.88	59.51
TSk1	136.97	147.83	167.55
SNPCP1/H2O	80.31	83.16	103.06
	Mechanism k2
SNP + CP1	0.00	0.00	0.00
SNP/CP2	−9.69	−7.87	43.71
TSk2	92.87	97.24	120.36
SNPCP2/H2O	40.06	43.46	66.56
	Mechanism k3
SNP + CP1	0.00	0.00	0.00
SNP/CP3	−9.69	−7.87	43.71
TSk3	44.48	47.54	65.67
SNPCP3/H2O	−26.88	−32.38	−15.24

CP: cyclophosphamide; SNPs: superparamagnetic iron oxide nanoparticles.

Scheme 2 demonstrates mechanisms k₁ and k₂ for the covalent functionalization of CP onto the SNP. In these reactions, the surface H₂O of the SNP is substituted by the Cl and P=O groups of CP to give products SNPCP1-2/H₂O (Figure 5).

Scheme 2.

Mechanisms k₁ and k₂.

Figure 5.

Optimized structures of SNPCP1/H₂O and SNPCP2/H₂O.

The transition states of step k₁ (TS _{k 1} ) and step k₂ (TS _{k 2} ) were optimized by using reactants SNP/CP1-2 and products SNPCP1-2/H₂O (Figure 6). Using Table 3, $E_{\mathrm{a}}$ , $\Delta H^{‡}$ , and $\Delta G^{‡}$ for steps k₁ (k₂) were 136.97, 147.83, and 167.55 kJ mol⁻¹ (92.87, 97.24, and 120.36 kJ mol⁻¹).

Figure 6.

Optimized structure of TS _{k 1} and TS _{k 2} .

The activation energy for mechanism k₃ is lower than for mechanisms k₁ and k₂ by 92.49 and 48.39 kJ mol⁻¹, respectively. The product of pathway k₃ (SNPCP3/H₂O) is more stable than those of pathways k₁ and k₂ (SNPCP1-2/H₂O). In contrast to the paths k₁ and k₂ which are endothermic and nonspontaneous, the reaction related to mechanism k₃ is spontaneous (ΔG = −111.28 kJ mol⁻¹) and exothermic (ΔH = −168.97 kJ mol^–1). The energy barriers show that covalent functionalization can occur through NH in a six-membered ring. At room temperature, the activation energies related to mechanisms k₁ and k₂ are too high for covalent functionalization to take place through these pathways.

Conclusion

Two configurations of noncovalent functionalization of SNPs with CP were investigated at the B3LYP and M06-2X density functional levels in the gas and solution phases. The SNP was modeled using the Fe₆(OH)₁₈(H2O)₆ ring cluster. The values of the solvation and binding energies show that these noncovalent interactions (SNP/CP) are energetically favorable. The values of global hardness and HOMO–LUMO energy gap related to CP are higher than those of SNP/CP1-2,3, showing the reactivity of CP increases in the vicinity of the SNP.

We studied three possible mechanisms of covalent functionalization of the SNP with CP thorough Cl (mechanism k₁), PO (mechanism k₂), and NH (mechanism k₃) groups. The activation parameters related to mechanism k₃ are lower than those of mechanisms k₁ and k₂. Pathway k₃ is also spontaneous and exothermic. Therefore, our calculations show that mechanism k₃ provides the possibility of creating a covalent bond between CP and SNP, while mechanisms k₁ and k₂ are not suitable for this task due to their high energy barriers.