Computer simulations use the dissipative particle dynamics (DPD) technique (48), which extends the simulation scales of time and space to be appropriate to the study of nanoparticle-membrane systems with explicit water. The models of lipid, membrane, and GO are shown in fig. S6. The model of the amphiphilic lipid was constructed by a head group with three hydrophilic beads and two tails consisting of three hydrophobic beads. A total of 625 lipids self-assembled into a tensionless lipid bilayer membrane spanning the simulation box. Each GO was modeled by arranging the hydrophobic beads on a single layer of a face-centered cubic (fcc) lattice into a desired geometrical shape and size (29, 49). The modulus of the GO model was calibrated according to the experimentally found elasticity of graphene (49, 50).

In particular, the interaction parameter between GO and lipid tails, χGT, is varied to reproduce different oxidization degrees or chemical modifications of the GO. For example, increasing χGT indicates a higher oxidization degree of the GO due to the reduced attraction between GO and lipid tails. Upon interacting with the lipid bilayer membrane, the GO model leads to structures and dynamic behaviors similar to those constructed based on the typical structure model representing outcomes from standard oxidization processes (see figs. S7, S8, S14, S15, and S19, and movies S1 and S2) (29, 51, 52). Furthermore, the results based on such a model are readily generalized to other 2D nanomaterials.

The size of our simulation box is 20 × 20 × 20 rc3 and periodic boundary condition in all directions is taken into account, where rc = 0.7 nm is the cutoff distance. To exclude the effect of system size on the diffusion of GO, we also performed simulations with a box size of 40 × 40 × 40 rc3. All systems were pre-equilibrated for the first 104 τ to confirm the equilibrium of the GO-sandwiched structures, while the production trajectories of the sandwiched GO are obtained from succeeding 4 × 104 τ simulations. Here, τ ≈ 7.7 ns and is the time unit used in the simulations.

In addition, to compare the efficiencies of drug delivery from a sandwiched GO and the intracellular region, we built a double-bilayer system, which divides the system into two regions: an “extracellular” region without drug bead and an “intracellular” region where the drug beads can be added into it (fig. S6). Each receptor, which will be targeted by the drug beads, is modeled as a cluster of frozen DPD beads grouped into a rigid body with fcc-arranged beads (53). Two pieces of lipid membranes have a total of 1952 lipids, with each membrane having 976 lipids. The size of such a simulation box is 25 × 25 × 60 rc3. The lower membrane is 10 rc away from the bottom of the box, while the upper membrane is 20 rc away from the top. Drug beads are represented by a single DPD bead.

More details on the simulation methods, models, and data analysis are given in section S1.

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