To predict the co-adsorption of DOX/PTX on the DMAA-TMC functionalized C60, utilizing various computer-based mechanisms, co-release, and aggregation of drugs were investigated in cancerous and physiological conditions with pHs 5.5 and 7.4, respectively.
Drug-C60 Accumulation
Gyration radius (Rg) is a factor that enables us to analyze the aggregation and stability of molecules such as polymers and resizing of biological macromolecules such as proteins over time (39). The average of the gyration radius at initial and final time is shown in Table 1 and 2. As shown in Table 1, the gyration radius indicates the accumulation of molecules in one region. The low Rg indicated a high accumulation in the location. The Gyration radius of DOX and PAX is about 3 nm, indicating the aggregation radius of drug accumulation on the C60 surface. Due to the dimensions of C60 and simulation boxes, a useful aggregation of drugs is formed around the C60. This revealed that the polymer molecules are clustered together in this simulation. PAX also has a lower radius than DOX, indicating a better accumulation of DOX in comparison to PAX. Complexation due to the accumulation of PAX molecules is more stable and concentrated. The interaction of hydrophilic polymer DMAA with water molecules and C60 helps to coat the nanocarrier better in bloodstream, which can improve the hydrophilicity of PAX. According to Table 1 and 2 the accumulation of the same drugs is similar in two different pHs states at initial time.
On the other hand, the higher the gyration radius, the greater dispersion between the particles. As shown in Table 2, At acidic pH the Rg increase, the stablitly and aggregation of systems decrease , and the system disassembled. Hence, the release of drugs facilated at acidic envirment
Drug-nanocarrier interaction
Hydrogen bonding between two atoms is defined as a donor-acceptor pair with an angle between them less than 30 degrees. The Fig.1 show changes in the numbers of hydrogen bonds over time between polymer-polymer and polymer-drug and C60-drug for all three simulations are shown in Fig.1. Hydrogen bonding can serve as a hydrophilicity indicator of the carrier. Besides, hydrogen bonding is part of the interatomic forces that can contribute to carrier strength and stability. The analysis of the diagrams below shows that DOX is not bounded to C60s but has many hydrogen bonds with DMAA-TMC. This chart illustrates the crucial role of DMAA-TMC in this drug delivery system. DMAA-TMC interacts and bonds with C60, which makes it more hydrophilic. C60s and DOX, as well as PAX, are hydrophobic compounds, and this is a significant drawback for drug carriers; Because hydrophobic compounds aggregate in water and compose large particles disrupting drug delivery and block the bloodstream.
Furthermore, DMAA-TMC has solved this problem by hydrophilic the complex. The graphs also show that PAX did not form hydrogen bonds with C60s, while PAX makes many hydrogen bonds with DMAA-TMC, which is an essential factor in drug delivery. A comparison between PAX and DOX Shows that the DOX-DMAA-TMC hydrogen bonds are more robust than the PAX-DMAA-TMC hydrogen bonds. Therefore, the addition of DMAA-TMC also contributes to better adsorption of DOX as the hydrogen bonds between DOX and DMAA-TMC are relatively stable.
3- Energy Interaction of Drug and Carrier
Neutral state; pH=7.4
In the Fig.2 and Fig.3, the interaction of the DOX molecule with C60 is investigated. At neutral pH, electrostatic energy plays a significant part in the total interaction energy. While in the acidic state, the electrostatic energy is zeroed, and the van der Waals energy has a considerable share of the total interaction energy. That is due to the surface charge of the carboxyl functional groups at the C60 surface. The carboxyl group has a negative charge at neutral pH and no charge at acidic pH.
On the other hand, DOX has a positive charge at neutral pH and acidic pH. As a result, in the neutral state, drug, and C60 functional groups, have anonymous and robust electrostatic interactions. The higher the electrostatic energy at neutral pH, the higher the adsorption of the drug onto the nanocarrier surface at this pH. The critical point is that the drug at a neutral pH, which is the pH of the blood, can transfer satisfactorily to the surface of the C60. and C60, by having a strong attraction to DOX, can serve as an excellent carrier for the drug.
Fig.2 shows the interaction between DOX and DMAA-TMC , as can be seen in figure c., the van der Waals interaction is close to zero. Still, there is a significant negative electrostatic interaction between the drug and the polymer. This interaction is due to the positive charge of DOX and the negative charge of the polymer at this pH. The negative electrostatic energy indicates a strong attraction between the drug and the DMAA-TMC. DMAA-TMC is an essential aid in the absorption of the drug.
The part b. in Fig.2 is the energy interaction of PAX with C60. As shown in the figure at neutral pH, the electrostatic energy shows a more significant number, while the energy van der Waals energy is close to zero. C60 is functionalized with carboxyl functional groups. The carboxyl group has a negative charge at neutral pH and no charge at acidic pH. On the other hand, PAX has zero charges at neutral pH. As a result, in the neutral state, the electrostatic energy between PAX and the C60 is close to zero. Van der Waals Energy plays a significant part in the adsorption of PAX onto C60. The following diagram illustrates the energy interaction between PAX and DMAA-TMC at d. As shown in Fig.2, at neutral pH, van der Waals energy shows a more significant number, and electrostatic energy is nearby to zero. PAX has zero charges at neutral pH. As a result, in the neutral state, the electrostatic energy between PAX and DMAA-TMC is close to zero. van der Waals energy plays a significant role in the absorption of PAX onto DMAA-TMC.
Cancerous state pH=5.5
In Fig.4, the interaction energy of the doxorubicin molecule with C60 is investigated. As shown in the figure at acidic pH, the electrostatic energy is shallow and close to zero. At acidic pH, electrostatic energy is zero, and van der Waals energy has a significant contribution to the total interaction energy. This is due to the surface charge of the carboxyl functional groups at the C60 surface. On the other hand, DOX has a positive charge at neutral pH and acidic pH. As a result, in the neutral state, C60 and drug functional groups have nameless charges and find durable electrostatic interactions. Though, at acidic pHs since C60 and carboxyl group charge becomes zero, the electrostatic interaction energy between C60 and DOX is also zero.
Fig.4.b. Shows the van der Waals and electrostatic energies of PAX and C60. As is clear from the figure, the electrostatic energy is close to zero, and the total energy is approximately equivalent to the van der Waals energy. The zero electrostatic energy is due to the zero charge of the carboxyl group at acidic pH. However, the surface charge of paclitaxel is also close to zero. Therefore, the electrostatic interaction between paclitaxel and C60 is zero, and the van der Waals interaction is fragile. The weak interaction energies lead to a better release of the drug from C60 and are considered a decisive factor for the carrier, which can be very useful in drug release.
Fig.4 c. Shows the interactions between DOX and DMAA-TMC. The interesting point in the below diagram is that the interaction between the drug and the DMAA-TMC in an acidic state has positive electrostatic energy. This means that there is a repulsion between chitosan and the drug, and this is very effective in releasing the drug. Repulsion between DMAA-TMC and the drug causes a better release of the drug from the surface of the DMAA-TMC and C60. In fact, besides biocompatibility and hydrophilicity, DMAA-TMC plays a significant role in the mechanism of drug release in cancer tissue.
The figure 4 shows the interaction between DOX and DMAA-TMC. As can be seen from the figure, the van der Waals interaction is close to zero, but there is a significant negative electrostatic interaction between the drug and the DMAA-TMC. This interaction is due to the positive charge of DOX and the negative charge of DMAA-TMC at this pH. The negative electrostatic energy indicates a strong attraction between the drug and the DMAA-TMC. DMAA-TMC is an essential aid in the absorption of the drug.
Fig.4 d. Shows the interaction energy between PAX and DMAA-TMCin an acidic state. As can be realized from the picture, the electrostatic interaction with van der Waals is zero between the drug and the chitosan, which contributes to drug release. Zero electrostatic energy is due to zero surface charge of PAX.
Drug release mechanism
As shown at Fig 6. Imine group includes a double bond between nitrogen and carbon atoms. The PAX/DOX-loaded nanomaterials via imine linkage could persevre drugs at physiological environment in the system and disassemble at acidic pH through the cleavage of imine bonds, which would face to immediately release DOX/PAX (40).
Validation test
To validate the computational procedure, a relevant recent article was chosen to reproduce a part of Gibbs free energy (∆G) calculation (38). This article has studied the co-delivery of DOX/PAX by a nanotube-chitosan carrier. The average value of ∆G is -20.75 kcal/mol in the reference work for DOX adsorption on chitosan-nanotube (in acidic pH) . The umbrella sampling simulation in GROMACS software was used to reproduce these data. Simulation results yielded a ∆G value of -21.64 kcal/mol that was near that of the reference study. These measurements can provide proof of this work and show consistency with previous works (38).