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Graphene, a two-dimensional nanomaterial with unique biomedical properties, has attracted great attention due to its potential applications in graphene-based drug delivery systems (DDS). In this work graphene sheets with various sizes and graphene oxide functionalized with polyethylene glycol (GO-PEG) are utilized as nanocarriers to load anticancer drug molecules including CE6, DOX, MTX, and SN38. We carried out molecular dynamics calculations to explore the energetic stabilities and diffusion behaviors of the complex systems with focuses on the effects of the sizes and functionalization of graphene sheets as well as the number and types of drug molecules. Our study shows that the binding of graphene-drug complex is favorable when the drug molecules and finite graphene sheets become comparable in sizes. The boundaries of finite sized graphene sheets restrict the movement of drug molecules. The double-side loading often slows down the diffusion of drug molecules compared with the single-side loading. The drug molecules bind more strongly with GO-PEG than with pristine graphene sheets, demonstrating the advantages of functionalization in improving the stability and biocompatibility of graphene-based DDS.

The clinical use of various potent hydrophobic molecules, many of which are aromatic, is often hampered by their poor water solubility and low biocompatibility. Although water-soluble prodrugs may circumvent these problems, the efficacy of the drugs decreases. Nanomaterial-based drug carriers have become a hot spot of research at the interface between nanotechnology and biomedicine because the nanocarriers allow efficient loading, targeted delivery, and controlled release of drugs [

Tremendous efforts have been made on modification of graphene and its derivatives for various biomedical applications. Liu and coworkers [

Despite the experimental and theoretical studies mentioned above, the thermodynamics and kinetics of graphene-drug complex remain obscure at a molecular level. For noncovalent graphene-drug complexes, the major practical concerns are whether the drug molecules can be loaded onto the graphene sheets tightly. To design stable graphene-based drug delivery systems (DDS), therefore, it is necessary to investigate thermodynamics stability from binding energy point of view. Moreover, the diffusion behaviors of drug molecules on the graphene sheets can be used to measure the kinetic stability of DDS. In this work, we employed molecular dynamics method to study the interaction between graphene and drug molecules focusing on the various sizes of graphene sheets as well as the types, numbers, and loading modes of drugs. Specifically, we studied four types of anticancer drug molecules (CE6, DOX, MTX, and SN38, shown in Figure

Atomic structures of graphene-drug complex D_{1}@Gf_{20}. The radius of gyration

(CE6_{1})@Gf_{20}

(DOX_{1})@Gf_{20}

(MTX_{1})@Gf_{20}

(SN38_{1})@Gf_{20}

To study the size effects of graphene, we built graphene sheets with a variety of sizes: a periodic graphene sheet, five squared H-terminated graphene sheets with a side length, is 10 Å, 20 Å, 30 Å, 40 Å, and 50 Å, respectively. The periodic GO-PEG complex was constructed for studying the effects of surface functionalization. We built graphene-drug complex models initially by “adsorption locator” module implemented in Materials Studio [^{−5 }kcal/mol of energy and 0.001 kcal/mol/Å of force were used.

Typical atomic structures of graphene-drug complexes (a) CE6_{8}@Gf_{50}, (b) DOX_{8}@Gf_{50}, (c) MTX_{8}@Gf_{50}, and (d) SN38_{8}@Gf_{50}. The dashed line in the figure presents the intermolecular or intramolecular hydrogen bonding interaction of drug molecules.

(CE6_{8})@Gf_{50}

(DOX_{8})@Gf_{50}

(MTX_{8})@Gf_{50}

(SN38_{8})@Gf_{50}

To investigate the dynamic process of drug molecules on the graphene, we performed molecular dynamic (MD) simulations to elucidate the absorption behavior of drug molecules. On the basis of the geometry optimization, we first carried out the simulations at the constant volume and constant temperature (NVT) ensemble (

The binding energy (

Average binding energy is an integrated representation of binding strength between drug molecules and graphene. In order to further understand the binding energy, we calculate the instantaneous interaction energy, instantaneous deformation energy, and instantaneous binding energy using the last snapshot structures of NVT simulations. These energy components are defined as follows:

After NVT simulations reach equilibrium, we used the final frame structures of NVT simulations as the initial structures to run NVE (constant volume and constant energy) MD simulations. The total simulation time was 500 ps with a 1 fs time step. The MD trajectories were printed out every 100 fs. To study the thermal diffusion behavior of drug molecules on the surface of graphene, we calculated the diffusion coefficient of drug molecules on the surface of graphene as follows:

To investigate the influences of sizes of graphene sheets on the binding strength of graphene-drug complexes, we load drug molecules on the squared graphene sheets with a variety of finite side lengths, for example, 10 Å, 20 Å, 30 Å, 40 Å, and 50 Å, as well as periodic squared sheets with a unit cell 50 × 50 × 20 Å modeling infinite large graphene sheets. The four types of drug molecules, namely, CE6, DOX, MTX, and SN38, are loaded, respectively, on either one side (D_{
n}@Gf_{
L}) or two sides [(D_{
n})_(D_{
n})@Gf_{
L}] of graphene sheets, where D_{
n} represent _{
L} or Gp_{
L} are finite or periodic graphene sheets with a length of _{1}@Gf_{
L}), or one drug molecule on each side of graphene sheets denoted as double-side loading mode [(D_{1})_(D_{1})@Gf_{
L}]. To evaluate the binding strength of graphene-drug complex, we discuss the results of binding energies and their components including interaction energies and deformation energies, respectively, as follows.

The average binding energy

Average binding energies (

Comparisons of

Instantaneous binding energies (

Instantaneous binding energies (

The in-plane diffusion coefficients, ^{2}/s) when loaded on the graphene sheet of 10–20 Å in both single-side and double-side modes, indicating that the movement of drug molecule is restricted within the small sized graphene sheets. The diffusion coefficients of drug molecules increase gradually as the graphene sheets become larger and approach towards the corresponding values on the periodic graphene sheets. This trend indicates that larger graphene sheets provide more free spaces for faster diffusion.

Average in-plane diffusion coefficients of one drug molecule loaded on the graphene sheets of 10–50 Å in (a) single-side and (b) double-side modes. The dashed lines represent the average in-plane diffusion coefficients of one drug molecule loaded on periodic graphene in (a) single-side and (b) double-side modes. The diffusion coefficients of four types of drug molecules CE6, DOX, MTX, and SN38 are shown in the figures, respectively.

The diffusion coefficients of drug molecules loaded on the periodic graphene sheets in the double-side modes are always smaller than those in the single-side modes except for CE6. This means that double-side loading often slows down the diffusions of drug molecules compared with single-side loading probably due to the interactions between the drug molecules separated by the graphene sheets. The diffusion coefficients of single molecules loaded on the periodic graphene sheets increase in the order of CE6 < DOX < MTX < SN38 in the single-side mode, while the diffusion coefficient increases in the order of DOX < CE6 < MTX < SN38 in the double-side mode.

The average binding energy

Average binding energies (

Instantaneous binding energies (

Instantaneous binding energies (

To understand the trend of the instantaneous binding energies, we decompose ^{2}). The larger drug coverage leads to almost invariant instantaneous deformation and binding energies, indicating that the stability of the graphene-drug complex is independent of the number of densely loaded drug molecules. The typical atomic structures of graphene-drug complexes exhibit the H-bonding and electrostatic interactions among drug molecules and vdW interactions between drug molecules and graphene sheets as shown in Figure

When multiple drug molecules are loaded onto the periodic graphene sheets, neither the instantaneous binding energies nor their components change significantly with the number of the drug molecules (Figure

Instantaneous binding energies (

To examine the effects of deformation energies and interaction energies of multiple drug molecules separately, we decompose further the deformation-interaction energies (

(a) Instantaneous deformation energies and (b) instantaneous interaction energies of different types and numbers of drug molecules loaded onto the periodic graphene sheets.

The average diffusion coefficients of multiple drug molecules on the surface of graphene sheets were calculated as the functions of the number of the drug molecules (Figure ^{2}), the diffusion coefficients become small, meaning that the drug molecules are locked. The diffusion coefficients of drug molecules loaded on the double sides of graphene are lower than those loaded on the single side, suggesting the dragging effect of molecular motion caused by the interactions between the drug molecules separated by the graphene sheets. Moreover, the drug molecules diffuse more quickly on the surface of periodic graphene than on the finite sized graphene sheets, indicating that the limited sizes of graphene sheets slow down the movement of drug molecules probably due to the boundary effects.

In-plane diffusion coefficients (

To investigate the effects of surface functionalization, we loaded drug molecules (_{
n}@GO-PEG complex are shown in Figure

(a) Average binding energies and (b) diffusion coefficients of D_{
n}@(GO-PEG) complex with various types and numbers of drug molecules in single-side loading modes.

(a) Atomic structure of GO-PEG complex. The GO-PEG is divided into four parts decorated by four types of functional groups (i) hydroxy, (ii) carboxide, (iii) epoxy group, and (iv) carboxyl, respectively. (b) Typical atomic structures of graphene oxide-drug complex CE6_{8}@GO-PEG (top view and side view).

GO-PEG

(CE6_{8})@(GO-PEG)

The in-plane diffusion coefficients (Figure ^{2}/s) and remain unchanged with the increase of the number of drug molecules. This suggests that the drug molecules on the GO-PEG sheets are almost immobile. Considering both the large binding energies and small diffusion coefficients discussed above, the GO-PEG-drug complexes are obviously more stable than the graphene-drug complexes. This can be understood by the fact that there are mainly vdW interactions between drug molecules and graphene in D_{
n}@G, while additional electrostatic and H-bonding interactions in D_{
n}@GO-PEG contribute to the stronger bindings.

In this work, molecular dynamic simulations were performed to investigate the energetic stabilities and diffusion behaviors of the graphene-drug complexes. We focus on the influences of the size of graphene sheets, the number and types of drug molecules, and the loading modes. Our simulations show that the binding strength of graphene-drug complex is mainly determined by the deformation of finite graphene sheets. When the areas that drug molecules occupy have comparable sizes as graphene sheets, for example, 20–30 Å/molecule, the deformation of graphene sheets is minimized and the graphene-drug bindings are the strongest. The average binding strength per molecule fluctuates between 10 and 70 kcal/mol that is not sensitive to the number and types of drug molecule as well as their loading modes. If the density of drug coverage is low and graphene sheets are relatively large, the binding strength is mainly determined by the interaction of graphene-drug. The limited sizes of graphene sheets restrict the movement of drug molecules. Multiple drug molecules may form clusters that slow down the diffusion on graphene sheets. Diffusion in the double-side loading mode is often slower than that in the single-side loading mode. Compared with pristine graphene sheets, graphene oxide functionalized with PEG chains has stronger bindings with drug molecules so that the drug molecules are essentially immobilized. These results give physical insights into the stability and dynamics of graphene-drug complexes, helpful for designing novel graphene-based drug delivery systems.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful for financial support from “Shanghai Pujiang Talent” program (12PJ1406500); “Shanghai High-Tech Area of Innovative Science and Technology (14521100602),” STCSM; “Key Program of Innovative Scientific Research” (14ZZ130) and “Key Laboratory of Advanced Metal-Based Electrical Power Materials,” the Education Commission of Shanghai Municipality; State Key Laboratory of Heavy Oil Processing, China University of Petroleum (SKLOP201402001). Xinluo Zhao thanks National Natural Science Foundation of China (Grant nos. 51202137, 61240054, and 11274222). Computations were carried out at Hujiang HPC facilities at USST, Shanghai Supercomputer Center, and National Supercomputing Center in Shenzhen, China.