Interfacial Engineering of Smart Polymer Self-Assembly Using Doped-Nanostructures for Constructing Stable Nano-Carriers

Nowadays, nanotechnology has been developed in various �elds of treatment, including cancer treatment. Since the prevalence of different types of cancer has risen, and currently available cancer treatments such as chemotherapy and radiotherapy may cause serious side effects. In this regard, researchers have made considerable efforts to encourage the creation and make strides in treating this deadly disease. Meanwhile, nanotechnology has become widespread, and various nanomaterials, including nanoparticles, have been extensively used to transfer the drug to the targeted sites. Recently, many drug delivery systems have been developed based on nanoparticles, and various substances have been employed as drug stimulants or enhancers to improve the treatment effectiveness, stability, and safety of anticancer drugs. In this paper, the drug delivery capability of three new categories of carbon nanoparticles (i.e., Fullerenes, nanosheets, and Carbon Nano Tubes (CNTs)) was investigated by Molecular Dynamics (MD) simulation. Energy, Gyration Radius (Rg), Hydrogen bond (H-Bond), Radial Distribution Function (RDF), and Solvent Accessible Surface Area (SASA) analyses have been used to compare the studied nanoparticles. The Boron Carbon Nitride (BCN) nanosheet simulation exhibited the lowest drug particle Contact Area, the highest RDF, the most inferior reduction in the Rg, the highest number of H-Bonds, and the highest drug adsorption energy. Thus, BCN nanosheet was introduced as the best nanoparticle for drug delivery purposes.


Introduction
Nowadays, cancer has become one of the most common diseases worldwide 1 .Cancer is a consequence of the mutation in the cells.As mutated cells multiply more rapidly than normal ones, they can allocate more nutrients and oxygen, thus making supplements scares for the normal cells 2,3 .Moreover, transferring the drug to the cancer cell sites is a signi cant challenge in cancer treatment.Due to the fact that transferring anticancer drugs to the entire body may cause many complications; in addition, some cancer cells may develop resistance against anticancer drugs during chemotherapy.Elevation of the drug dose and co-administration of several drugs have been employed to resolve this problem; both these solutions, however, can increase the drug toxicity.Although anticancer drugs can kill cancer cells, they can also interfere with the growth and division of healthy cells.Impaired development of healthy cells may result in severe complications.When these drugs affect cancer cells, they temporarily reduce the number of blood cells, increasing the risk of infection and fatigue in the patient which in term give rises to other diseases [4][5][6][7] .
Drug transmission is a vital part of medicine and treatment.Drug delivery systems (DDS) have been created to make strides in the therapeutic properties and pharmacological of drugs utilized among cancer patients 8 .DDS is capable of releasing a speci c amount of drug in a particular site, hence, reducing the side effects while enhancing the drug e cacy.Furthermore, DDS can increase the chance of drug uptake by cancer cells, prevent premature breakdown of the drug in the body, and maintain drug concentration during treatment by controlling the rate of drug release 9,10 .To prevent side effects, a wide variety of DDS systems have been developed for the drug accumulates in the target site 11 .
In recent years, increasing attention has been paid to nanostructured carriers' preparation for drug delivery, as these structures are smaller than the cell and can control and slow down the drug release and protect the drug molecule.The ability of the DDSs to overcome the biological barriers can increase the drug persistence in the bloodstream.In this regard, targeted drug delivery and biocompatibility can be considered the crucial advantages of drug delivery systems 12 .Over the past half-century, advancements in polymer science, chemistry, biology, and mechanical and physical sciences have resulted in the development of various nano-carriers with unique features and versatile performances.In general, pharmaceutical carriers can be classi ed into two main groups: organic and inorganic carriers.
Various materials such as polymers, metal particles, and lipids have been used to fabricate nano-carriers to transfer drugs.Nano-carrier-based drug delivery systems have now entered the global pharmaceutical market, and their application in drug delivery is increasing day-by-day and nanoparticles have become very popular in various elds of biology and medicine.Since these nanoparticles size are in the range of 100 nm, they can be loaded with a wide range of drugs such as small hydrophobic and hydrophobic drugs, vaccines, and biological molecules [13][14][15][16] .Moreover, nanoparticles can likewise improve treatment and diagnosis.In this regard, Carbon Nano Tubes (CNTs) have been utilized as nano-carriers to deliver the drug to the target site 17,18 .Due to the small sizes, these particles can easily pass across the cell membranes and biological barriers.They also possess a high surface area and their surfaces can be modi ed by various functional groups.This in turn yields to enhance their solubility and biocompatibility, and the conductivity of different materials.These nano-carriers can carry other biological molecules such as proteins, DNA, and pharmaceutical agents loaded on their surface or inside the porous of the structures.Simultaneous targeting and transfer of two or more compounds is another essential feature of these particles [19][20][21] .The most common nano-carriers are in the form of polymers.For the controlled drug release, these polymers must be biocompatible and non-toxic with no leak or impurity.Physically, they must be well-structured with the desired half-life.Polymers used in the manufacturing of polymer nanoparticles can be synthetic or natural.Polymeric nanoparticles are frequently chosen from biodegradable sorts.The advantage of using polymer nanoparticles lies in their high stability and scalability.The Nano-carriers transfer the required drugs in two ways: 1-Carrying the imprisoned agents (encapsulation) 2-delivering the drugs absorbed on the nanoparticle surface.Polymer nanoparticles are small-sized stable colloidal systems.The drug is either physically distributed in polymer nanoparticles or chemically bonded to its main polymer chain.Increasing the solubility and stability of drugs is one of the advantages of using polymer nanoparticles.Therefore, polymer nanoparticles are among the most widely used drug delivery systems [22][23][24][25] .
So far, a wide diversity of polymers have been used as polymer nanoparticles.In polymer nanoparticles' synthesis, Poly (lactic-co-glycolic acid) (PLGA) is used.European Medicines Agency (EMA) and the Food and Drug Administration (FDA) approved the biocompatibility and biodegradability of PLGA [26][27][28] .Poly (ethylene glycol) (PEG) is a chemical compound made by repeating ethylene glycol units.PEG has found numerous medical industry applications; thanks to its non-toxicity, biocompatibility, and water-solubility, its pharmaceutical and biomedical applications are continuously expanding [29][30][31] .
Ribo avin is one of the vitamin B family, which plays an essential role in several body activities, including cell growth.Ribo avin can naturally be found in milk, meat, eggs, forti ed our nuts, and green vegetables.The cancer cells have exhibited too high ribo avin uptake.Thus, it can signi cantly contribute to delivering the drug to cancer cells.In this context, scientists combined ribo avin to anticancer drugs and mounted it onto a carrier such as nanoparticles to treat cancer cells.Cancer cell membrane receptors can absorb ribo avin [32][33][34] .
A successful transport of the drug to the cancer cell requires strong adsorption between the drug and the nanoparticle.The use of MD simulation makes it possible to investigate the adsorption capacity of drugs by different nano-carriers.As the experimental evaluation of DDS performance could be complicated, time-consuming, and expensive, and the molecular dynamics (MD) simulation is an excellent tool capable of examining the drug-Nano-carrier interactions under different conditions.In this paper, the transfer of Doxorubicin (DOX) along with ribo avin by carbon nanoparticles and PEG and PLGA polymeric nanoparticles was investigated for the rst time.Rezvantalab et al.Reported the best concentrations of PLGA and PEG polymers for drug delivery to the target area at a ratio of 8:2 35 .In this paper, PLGA and PEG are combined at a ratio of 8:2.Fullerene, nanosheets, CNTs, and their derivatives have also been used as part of the Nano-carrier.The energy, Hydrogen bond (H-bond), Gyration Radius (Rg), Solvent Accessible Surface Area (SASA), and Radial Distribution Function (RDF) analyses were employed to analyze the adsorption power of various simulated Nano-carriers.

Methods
The molecular structure of DOX was obtained from rcsb.org.The initial molecular systems of Fullerene, nanosheet, and CNTs were designed by Nanotube_Modeler_1.7.9 36,37 .The molecular systems of Boron Carbon Nitride (BCN) nanosheet, BCN nanotube, and BCN Fullerene were developed by Avogadro software by adding N and B atoms molecular structure of the mentioned systems.Replacing 10% of carbon atoms with nitrogen atoms create Nitrogen-doped (N doped) Graphene, N doped nanotube, and N doped Fullerene molecular structures.The Phosphorus doped (P doped) Graphene, P doped nanotube, and P doped Fullerene molecular structures were created by Avogadro software by adding phosphorus atoms to the molecular structure of nanosheets, CNTs, and Fullerene.Then, the molecular structures were optimized with Gaussian 09 38,39 software.To calculate the charge distribution of atoms, the Density Functional Theory (DFT) method was used through the B3LYP functional and 6-31G basis set.
The topology of these two-dimensional structures was then obtained by applying esp charges calculated from the Gaussian software and by the x2top command for the OPLSAA force eld 40,41 .The size of the simulation boxes was set 3 x 3 x 30 nm 3 .We then placed the built-in molecular structures in the simulation boxes and add 30600 (SPC / E water model) water molecules to each box.
We performed the simulation in 4 steps.Initially, we did the optimization at 50,000 2-fs steps, followed by the optimization phase's energy level was set at 10kj/mol.Then an NVT simulation was performed for 500 ps to balance the simulation box's temperature at 300 K by the V_rescale algorithm [42][43][44] .In the NPT stage, the simulation box pressure was balanced at 1 bar by the parrinello_rahman algorithm [45][46][47] in at 500 ps.In the end, considering the H-bond, cut-off radius of 1.4 nm, the last simulation was performed by the lincs algorithm at 100 ns.Energy, Rg, H-bond, RDF, and SASA analyses were also performed for different simulations.

Results
Investigation of polymer micelle Compactness by using analysis of Rg: In this paper, the polymer micelles are applied to transmit the drug.The higher the compaction of micelle particles around the drug, the more likely the drug transfer to the target cells.Accumulation of polymer micelles around the drug prevents the drug from release to unwanted regions.Lower nal Rg (compared to the initial Rg) indicates better drug surroundings by micelles.Figure 1 shows the accumulation of polymers by a reduction in the Rg after 100 ns.Condensation of the polymer reduced the oscillations of the polymer particles.The compactness of polymer particles also declined the Rg and further stabilized the system.For comparing the simulated systems' stability, the difference between the initial and nal Rg was studied.One of the essential analyzes in polymer simulations is the Rg analysis, since Rg analysis indicates the accumulation of polymer particles around its center of gravity at different times.9][50][51][52] ; re ecting that the drug is surrounded by micelles for transfer to the body.In case the (r i -r cm ) communicates the separate between the particle i and the center of mass of the particle, at that point the Rg from the connection 1 is calculated.
Table 1 shows the difference between the initial and nal Rg for BCN Fullerene, Fullerene, N doped Fullerene, and P doped Fullerene simulations.Figure 2 indicates the Rg values for the same materials are plotted versus the simulation time.Consequently, Fig. 5 depicts the values of the nal Rg, which shows the lowest value in the BCN nanosheet simulation.The lower nal Rg in the BCN nanosheet simulation indicates more reduction in the Rg in this system.The Rg diagrams of BCN Fullerene and P doped Fullerene simulations show the variations in their Rg.However, Fullerene exhibits an increasing trend in the Rg.Despite of a decreasing trend in the Rg value of the N doped Fullerene during 5-60 ns interval, a sudden increase in the Rg at 60-80 ns range prevented a signi cant reduction in the nal Rg.The BCN Fullerene shows the highest reduction in the nal Rg.Polymers exhibit the highest accumulation in BCN Fullerene simulation with a decrease in the Rg of 1.16263 nm.In BCN Fullerene, the drug was more surrounded by polymer micelles giving rise to higher stability.A 0.9833 nm reduction was detected in the Rg of the P doped Fullerene.After the BCN Fullerene simulation, the highest accumulation of polymer particles occurred in the P doped Fullerene simulation.Among Fullerene systems, BCN Fullerene polymeric micelle exhibits the most increasing stability for drug delivery.
Table 2 shows the difference between the initial and nal Rg for BCN nanosheet, Graphene, N doped Graphene, and P doped Graphene systems.Figure 4 also presents the graph of the Rg vs. the simulation time, while Fig. 5 shows the values of the nal Rg.The nal Rg has the lowest value in the BCN nanosheet simulation, re ecting a higher Rg reduction.A sudden increase in the Rg occurring in 90-95 ns for the BCN nanosheet and P doped Graphene systems failed to prevent a reduction in the nal Rg in these simulations.Although the Rg was increasing through th simulation, a sudden decrease in the Rg at the interval of 95-100 ns affected the nal Rg compared to its initial value.BCN nanosheet simulation offered the most considerable reduction in the nal Rg.Polymers showed the highest accumulation in BCN nanosheet simulation, with Rg reduction of 1.40905 nm.The proliferation of polymer particles in the BCN nanosheet system reduced the polymer particles' oscillations and increased the simulated system's stability.In BCN nanosheet, the drug was more surrounded by polymer micelles and hence reach more stability.The reduction in the Rg of the P doped Graphene simulation was 1.27934 nm.After the BCN nanosheet, the highest accumulation of polymer particles occurred in the P doped Graphene system.Thus, among nanosheets, BCN nanosheet drug delivery is most stable.
Table 3 shows the difference between the initial and nal Rg of BCN nanotube, CNT, N doped nanotube, and P doped nanotube simulations.Figure 6 also demonstrates the Rg values vs. the simulation time, while Fig. 7 shows the nal Rg values.The lowest nal Rg was obtained in BCN nanotube, indicating a higher reduction of Rg in this system.The Rg value for N doped nanotube and P doped nanotube systems increase over the simulation time.A signi cant enhancement was observed in the Rg of N doped nanotube in the 35-60 ns interval.In N doped nanotube and P doped nanotube simulations, the nal Rg value increased compared to their initial values.However, the Rg diagram in CNT systems shows a decreasing trend most of the time.The Rg dramatically increased in the BCN nanotube in 30-55 ns interval, but a sudden decrease in the Rg in 85-100 ns affected the nal Rg compared to its initial value.BCN nanotube exhibited the most considerable reduction in the nal Rg.Polymers have the highest accumulation in BCN nanotube simulation with a 1.17895-nm reduction in the Rg.The accumulation of polymer particles in the BCN nanotube reduces the polymer particles' oscillations and increases the stability of the system.As a result, polymer micelles more surrounded the drug; thus it is more stable.The reduction in the Rg in the CNT simulation was 0.91054 nm.After the BCN nanotube, the highest accumulation of polymer particles occurred in the CNT simulation.Among the simulated CNTs, drug delivery by polymer micelle in BCN nanotube has the best stability.
The reduction in the Rg of the BCN nanosheet, BCN nanotube, and BCN Fullerene was 1.40905, 1.17895, and 1.16263 nm, respectively.BCN nanosheet exhibited the most massive reduction in the Rg value among all the simulated materials.The most signi cant decrease in the Rg occurred in BCN nanosheet which lead to the highest accumulation of polymer particles around the polymers' center of gravity.A successful delivery of the drug requires the drug to be surrounded by polymer micelles and the simulated BCN nanosheet, was well covered the drug.Moreover, the higher accumulation of polymer particles in the BCN nanosheet simulation results in fewer oscillations of the polymer particles and, hence, it increases the simulated system's stability.After BCN nanosheet, the highest accumulation of polymer particles occurred in BCN nanotube and BCN Fullerene simulations, respectively.Based on the Rg analysis, BCN nanosheet, BCN nanotube, and BCN Fullerene are the best nanoparticles for drug delivery purposes.

Investigation of drug-Nano-carrier hydrogen interactions:
Hydrogen bonding is the strongest intermolecular bond.Hydrogen atoms can form H-bonds in small atoms with high electron a nities such as oxygen and nitrogen.The number of H-bonds between the molecules in the simulation is a good indicator of the simulated systems' interactions.The high hydrogen bonding indicates strong intermolecular interactions.A strong drug-carrier interaction can result in proper drug transfer while preventing drug release in unwanted sites.A strong interaction should be formed between the drug and the polymeric nano-carrier to transfer the drug to target cells [53][54][55] .In this regard, the H-bond analysis can examine the number of H-bonds formed during the simulation time.
Table 4 shows the mean number of H-bonds between drug and polymer micelles during 100 ns of simulation for BCN Fullerene, Fullerene, N doped Fullerene, and P doped Fullerene systems.Over time, more H-bonds formes between drug and micelle in the BCN Fullerene system.Followed by BCN Fullerene, P doped Fullerene, N doped Fullerene, and Fullerene systems in the term of the number of H-bonds.BCN Fullerene provides better hydrogen bonding conditions between the drug and micelle, suggesting stronger micelle-drug, further enhancing the stable drug transfer to the targeted site.Among Fullerenes, BCN Fullerene provides the best conditions for drug delivery.
Table 5 shows the average number of H-bonds formed between drug and polymer micelles over 100 ns of simulations for BCN nanosheet, Graphene, N doped Graphene, and P doped Graphene systems.Over time, more H-bonds formed between the drug and the micelle in the BCN nanosheet system.After this system, P doped Graphene and N doped Graphene showes the highest H-Bonds, respectively.BCN nanosheet offered better conditions for hydrogen bonding between drug and micelle.The greater the number of H-Bonds, the stronger the micelle-drug interactions.Hence, the drug transfer to the target site become more stable.Among the studied nanosheet, BCN nanosheet exhibited the best drug delivery conditions.
Table 6 shows the mean number of H-Bonds between drug and polymer micelles during 100 ns of simulation for BCN nanotube, CNT, N doped nanotube, and P doped nanotube systems.Over time, more H-bonds were formed between drug and micelle in the BCN nanotube system.After that, the highest number of H-bonds were found in the CNT, N doped nanotube, and P doped nanotube, respectively.BCN nanotube provided better conditions for hydrogen bonding, re ecting stronger micelle-drug interactions.Stronger micelle-drug interaction can further enhance the stable drug transfer to the target site.Among CNTs, BCN Nanotube offered the best drug delivery conditions.
The average number of H-Bonds in BCN nanosheet, BCN nanotube, and BCN Fullerene simulations were 3.972, 2.63, and 2.207, respectively.More H-bonds were formed in the BCN nanosheet system; thus, this system can offer the best hydrogen bonding conditions between micelles and drugs.The improved conditions for hydrogen bonding in the BCN nanosheet simulation can strengthen micelle-drug interactions.Based on the H-bond analysis, BCN nanosheet is the best carbon-based system for targeted drug delivery.

Investigation of the ability to absorb drug by nano-carriers:
The nano-carrier's job is to deliver the drug to the targeted area and prevent it from being released in other parts of the body.The stronger the drug and the nano-carrier's attraction, the more the drug is absorbed by the nano-carrier and causes less release in unwanted parts of the body.Better drug adsorption indicates better drug delivery conditions as it re ects stronger interactions between the drug and the nano-carrier.Through RDF analysis, it is possible to study the distribution of molecules relative to a reference.RDF analysis shows the Nano-carriers' ability to absorb the drug.Polymeric micelles and carbon nanoparticles were considered as Nano-carrier in this paper [56][57][58][59][60][61][62] .
Table 7 shows the maximum RDF values for BCN Fullerene, Fullerene, N doped Fullerene, and P doped Fullerene systems.The BCN Fullerene system exhibites the highest drug uptake with a maximum RDF value of 3.701.After BCN Fullerene, P doped Fullerene, Fullerene, and N doped Fullerene offeres the second, third, and fourth highest drug uptake.The higher drug adsorption by BCN Fullerene shows stronger nano-carrier-drug interactions.The BCN Fullerene system provided better drug-nano-carrier interaction and hence improved the targeted drug delivery.
Table 8 shows the maximum RDF values for BCN nanosheet, N doped Graphene, and P doped Graphene systems.BCN nanosheet system showed the highest drug uptake, with a maximum RDF value of 3.876.After BCN nanosheet, P doped Graphene, Graphene, and N doped Graphene possessed the highest drug uptake, respectively.The BCN nanosheets enhanced drug adsorption, indicates the stronger interactions between the nano-carrier and the drug.Thus, this system can provide stronger for drug-carrier interaction and hence improved targeted drug delivery.
Table 9 shows the maximum RDF values for BCN nanotube, N doped nanotube, and P doped nanotube systems.BCN nanotube offered the highest drug uptake, with a maximum RDF of 3.781.After that, N doped nanotube, and P doped nanotube had the highest drug uptake, respectively.The BCN Nanotube's enhanced drug adsorption indicates the stronger interactions between the nano-carrier and the drug.Thus, this system can provide stronger for drug-carrier interaction and hence improved targeted drug delivery.
The maximum RDF values of BCN nanosheet, BCN nanotube, and BCN Fullerene were 3.876, 3.781, and 3.701, respectively.The BCN nanosheet presented the highest maximum RDF value, suggesting greater drug accumulation around the nano-carrier.After BCN nanosheet, drug aggregation around nano-carriers was highest in BCN nanotube and BCN Fullerene systems, respectively.BCN nanosheet managed to provide better conditions for stronger carrier-drug interaction.According to RDF analysis, BCN nanosheet is the best system for targeted drug delivery.
Contact area of drug particles in the presence of nano-carriers: Interactions between Nano-carriers and drugs cause Nano-carriers to absorb the drug and reduce the drug particles' contact surface.Further adsorption of the drug by the polymer nanoparticles reduces the drug contact with particles.Lower the average contact area of the drug particles result in better drug accumulation inside the nano-carrier.This in turn yields to better-targeted drug delivery conditions.
By the mean of SASA analysis, it is possible to check the contact area of different material particles.In this paper, we performed SASA analysis to investigate the area of contact between drug particles.Eq. ( 2) was used to calculate the contact area of drug particles.
Where, S (0) shows the amount of SASA analysis at the beginning of the simulation while S (t) indicates the amount of SASA analysis at different simulation times.In order to compare the contact area of drug particles for different systems, the mean values obtained from Eq. ( 2) are used.
Table 8 shows the mean contact area of drug particles over time in BCN Fullerene, N doped Fullerene, and P doped Fullerene systems.The BCN Fullerene system showed the lowest contact area (217,739).P doped Fullerene, N doped Fullerene, and Fullerene systems showed the least contact area, respectively.The lower contact area between drug particles in the BCN Fullerene system suggests a higher drug accumulation in the nano-carrier, leading to better-targeted drug delivery.The BCN Fullerene provided better conditions for the transfer of the drug to the target region.Table 9 presents the mean contact area of drug particles over time for BCN nanosheet, Graphene, N doped Graphene, and P doped Graphene.The BCN nanosheet exhibits the lowest contact area (214,642), followed by P doped Graphene, Graphene, and N doped Graphene, respectively.The lower contact area between drug particles in the BCN nanosheet system implies a higher drug accumulation in the nanocarrier, leading to improved targeted drug delivery.Among the simulated nanosheet, the BCN nanosheet provided better conditions for drug delivery.
Table 10 shows the mean contact area of drug particles over time for BCN nanotube, CNT, N doped nanotube, and P doped nanotube.The BCN nanotube offered the lowest contact area (216,716), followed by CNT, N doped nanotube, and P doped nanotube, respectively.The lower drug contact area in the BCN nanotube system shows a higher drug accumulation in the nano-carrier, leading to better-targeted drug delivery.Among the simulated CNTs, the BCN nanotube provided excellent conditions for drug transport to the target site.
The mean drug contact area was 214.642, 216.716, and 217.739 for the BCN nanosheet, BCN nanotube, and BCN Fullerene systems, respectively.The BCN nanosheet offered less contact area.In the case of the BCN nanosheet system, the lower contact area means the highest drug accumulation in the Nano-carrier, implying better drug delivery to the target region.The SASA analysis introduced BCN nanosheet as the best system for targeted drug delivery.
Investigation of van der Waals (vdW) and electrostatic bonds between drug and nano-carrier by using energy analysis: Chemical bonds hold molecules together temporarily or permanently.As intermolecular bonds are weaker than bonds between the and most well-known of these bonds are vdW and electrostatic bonds, vdW bonds arise from the induction of an electric eld from one atom's instantaneous dipoles to another and are known as vdW forces.At long distances (in nanometers), these forces attract and repel at close distances.Electrostatic bonds are formed due to the presence of opposite charges.The force between two atoms follows Coulomb's law with opposite charges.Successful drug delivery to the target region requires strong drug-Nano-carrier bonds.Energy analysis is one of the most fundamental indicators for comparing intermolecular interaction.By the energy analysis, it is possible to calculate the electrostatic and vdW forces' contributions in the intermolecular interactions.The stronger the intermolecular bonds, the greater the absolute value of the simulation energy [63][64][65][66] .Polymeric micelles and carbon nanoparticles were considered as Nano-carrier.The sum of the average energy from electrostatic and vdW bonds was considered the investigation criterion to investigate the strength of drug-Nano-carrier bonds.In this study, mmpbsa 67,68 software was utilized to calculate the energy contribution of electrostatic and vdW bonds.
Table 13 shows the average electrostatic and vdW energy in BCN Fullerene, Fullerene, N doped Fullerene, and P doped Fullerene systems.The BCN Fullerene system illuminates the highest absolute value of electrostatic energy (369, 4648) followed by Fullerene, P doped Fullerene, and N doped Fullerene, respectively.Furthermore, the highest absolute magnitude of vdW energy was found in the BCN Fullerene system (750, 7997), followed by P doped Fullerene, Fullerene, and N doped Fullerene, respectively.
Figure 8 shows the portion of drug-polymer micelles energy and the one between the drug and Fullerenes.The drug-polymer micelles energy predominated the total energy in all simulations.The drug-polymer micelles interaction was much stronger than the interactions between the drug and Fullerenes.BCN Fullerene showed the highest sum of vdW and electrostatics energy.Consequently, P doped Fullerene, Fullerene, and N doped Fullerene take the next places in this regard.The higher absolute value of vdW and electrostatic energy in the BCN Fullerene system indicates stronger drug-Nano-carrier interactions that prevent drug release to unwanted sites.Among the simulated Fullerenes, BCN Fullerene provided the best conditions for targeted drug delivery.
Table 14 shows the average electrostatic and vdW energies in BCN nanosheet, Graphene, N doped Graphene, and P doped Graphene systems.The P doped Graphene system showed the highest absolute value of electrostatic energy (632.12346),followed by the N doped Graphene, BCN nanosheet, and Graphene, respectively.The higher electrostatic energy in the P doped Graphene simulation implies the more vigorous the electrostatic bonds between the nano-carrier and the drug.The BCN nanosheet offered the highest absolute vdW energy (1100.595),followed by P doped Graphene, N doped Graphene, and Graphene, respectively.The greater absolute value of vdW energy in the BCN nanosheet system indicates the stronger vdW bonds between the carrier and the drug.Figure 9 shows the drug-polymer micelles energy portion and drug-nanosheet energy.In the P doped Graphene, the drug-polymer micelles energy did not signi cantly differ with the energy between the drug and the P doped Graphene.However, the drug-polymer micelles energy dominated in the other three simulations in Fig. 9.The total absolute value of vdW and electrostatic energies in the BCN nanosheet simulation was the highest, followed by the P doped Graphene, N doped Graphene, and Graphene simulations, respectively.The greater the absolute total energy in the BCN nanosheet system means stronger interactions between the drug and the polymercarrying nanomaterial which prevents the drug release in the unwanted sites.Among the simulated nanosheet, BCN nanosheet provided the best conditions for targeted drug delivery.
Table 15 shows the average electrostatic and vdW energy in the BCN nanotube, CNT, N doped nanotube, and P doped nanotube.The BCN nanotube showed the highest absolute electrostatic energy (370.32 followed by CNT, P doped nanotube, and N doped nanotube, respectively.The greater electrostatic energy in BCN nanotube implies stronger electrostatic bonds between the nano-carrier and the drug.The BCN nanotube also offered the highest absolute vdW energy (788.7657),followed by N doped nanotube, CNT, and P doped nanotube, respectively.The higher value of vdW energy in BCN nanotube simulation indicates the stronger vdW bonds between the Nano-carrier and drug.Figure 10 shows the contributions of drug-polymer micelle and drug-CNT energies to the total energy.The drug-polymer micelle energy predominated the total energy, suggesting that the drug-polymer micelle interactions are much stronger than the drug-nanotube interactions.It had the highest value in BCN nanotube simulation.After BCN nanotube, the absolute total energy was the highest in the CNT, P doped nanotube, and N doped nanotube systems, respectively.The higher absolute value of total energy in the BCN nanotube simulation indicates stronger drug-Nano-carrier interactions, preventing the drug release in the unwanted sites.Among the simulated CNTs, BCN nanotube provided the best conditions for targeted drug delivery.The sum of absolute vdW and electrostatic energies was 1480.815,1159.0857, and 1120.2646 for BCN nanosheet, BCN nanotube, and BCN Fullerene, respectively.As can be seen, the BCN nanosheet possessed the highest absolute total energy implying the most potent drug-Nano-carrier interactions, preventing the drug release in unwanted parts of the body and thus better drug transfer.The energy analysis introduced BCN nanosheet as the best nanoparticle for targeted drug delivery purposes.

Conclusion
The proper transfer of the drug to the cancer cells is of great importance in cancer treatment.Among different nano-carriers have been used to transfer the drug to the cancer cells.In this paper we examined various types of Fullerenes, nanosheets, and CNTs for drug transfer to cancer cells using MD simulations.We performed Rg, H-bond, RDF, SASA, and energy analyses for all systems.BCN Fullerene exhibited the largest reduction in the Rg.Thus, BCN Fullerene could be the best nanoparticle for drug transfer among the studied Fullerenes.This system also offered the highest maximum RDF, the lowest contact area, the highest number of H-bonds, and the largest drug adsorption energy.The results of energy, H-bond, RDF, and SASA analyses con rmed the result of Rg analysis.BCN nanosheet was introduced as the best nanosheet for drug transfer.It had the most considerable reduction in Rg, the highest maximum RDF, the lowest drug contact area, and the highest average number of H-bonds as well as the most signi cant drug adsorption energy.The results of energy, H-bond, RDF, and SASA analyses were in line with the Rg analysis ndings.BCN nanotube system exhibited the largest reduction in Rg.The BCN nanotube was selected as the best nanotube for drug transfer as it possessed the highest maximum RDF, the lowest drug contact, the largest average number of H-bonds, and the highest drug adsorption energy.The results of energy, H-bond, RDF, and SASA analysis con rmed the result of Rg analysis.In the studied categories, BCN Fullerene, BCN nanosheet, and BCN nanotube created the best drug delivery conditions for the target site, respectively.BCN nanosheet simulation showed the largest reduction in Rg, the largest maximum RDF, the lowest drug contact, the highest average number of H-bonds, and the highest drug adsorption energy.Therefore, BCN nanosheet is the best nanoparticle for drug delivery to the target area.It is also recommended to assess the transfer of DOX by a BCN nanosheet nanoparticle under laboratory conditions to investigate BCN effect of nanosheet over long periods of time.Table 3.The difference between the initial and nal Rg in different types of nanotubes.

Abbreviations
Table 4. Average number of H-Bonds formed between drug and polymer micelles in Fullerenes.
Table 5.Average number of H-Bonds formed between drug and micelles in Nanosheets.
Table 6.Average number of H-Bonds formed between drug and polymer micelles in CNTs.The nal Rg values of different types of Nanosheets.
Rg diagram of CNTs over 100 ns.
Page 26/29  The contribution of vdW and electrostatic energies in the average drug-polymer micelles energy and the average drug-Fullerenes energy within 100 ns.

Figures
Figures

Figure 3 The
Figure 3

Figure 7 Final
Figure 7

Table 2 .
The difference between the initial and nal Rg in different types of Nanosheets.

Table 7 .
Maximum RDF values of different types of Fullerenes.

Table 8 .
Maximum RDF values of various types of nanosheet.

Table 9 .
Maximum RDF values of CNTs.

Table 10 .
Average drug contact area for different types of Fullerenes.

Table 11 .
Average drug contact area for different types of nanosheet.

Table 12 .
Average drug contact area for different types of CNTs.

Table 13 .
Average energy of types of Fullerenes over 100 ns.

Table 14 .
Average energy of different nanosheets over 100 ns.

Table 15 .
Average energy of different nanotubes over 100 ns.