Tubulation and Aggregation of Spherical Nanoparticles Adsorbed on Vesicles

How nanoparticles interact with biomembranes is central for understanding their bioactivity. In this Letter, we report novel tubular membrane structures induced by adsorbed spherical nanoparticles, which we obtain from energy minimization. The membrane tubules enclose linear aggregates of particles and protrude into the vesicles. The high stability of the particle-filled tubules implies strongly attractive, membrane-mediated interactions between the particles. The tubular structures may provide a new route to encapsulate nanoparticles reversibly in vesicles.

Figure 1

(a) Bound minimum-energy state of two particles for the reduced volume $v=0.96$ of the vesicle and the rescaled adhesion energy $u\equiv U{R}_p^2/\kappa =2$ of the particle, where $U$ is the adhesion energy per area, $R_p$ is the particle radius, and $\kappa$ is the bending rigidity of the vesicle membrane. (b) Bound minimum-energy state of two particles for $v=0.92$ and $u=2.33$. (c) Bound state of three particles for $v=0.88$ and $u=2$. In (b) and (c), the particles are jointly wrapped by a membrane tube that invaginates into the vesicle.

Figure 2

Rescaled total energy $E/\kappa$ of a vesicle with two adsorbed particles as a function of the particle distance $r$ for the rescaled adhesion energy $u=2.33$ and the values $v=0.92$, 0.94, and 0.96 of the reduced volume. The particles with radius $R_p$ are in contact at the distance $r=2R_p$. The four snapshots represent minimum-energy conformations for the reduced volume $v=0.92$ at particle distances with $r/R_p=2$, 3.2, 6, and 9. Error bars represent the standard deviation of 10 simulations at each rescaled distance.

Figure 3

Rescaled binding energies $\Delta E/\kappa$ of two adsorbed particles as a function of the rescaled adhesion energy $u$ of the particles. The binding energy $\Delta E$ is calculated as the difference between the total energies $E$ at the particle contact distance $r=2R_p$ and at the distance $r=6R_p$, which approximates the location of the second minimum of the interaction profiles $E(r)$ shown in Fig. 2. Negative values of $\Delta E$ correspond to stable bound states of the particles. At the value $v=0.96$ of the reduced volume, the particles are symmetrically wrapped in their bound states as in the snapshot in the upper left corner. At $v=0.92$ and 0.94, the particles are bound together by a membrane tube as in the snapshot at the bottom of the figure.

Figure 4

Rescaled total energy $E/\kappa$ of a vesicle with three adsorbed particles bound together by membrane tubes as a function of the angle $\varphi$ between the particles for the reduced volume $v=0.88$ and the rescaled adhesion energy $u=2$. Here, $\varphi =0$ corresponds to a linear arrangement of the particles. The four snapshots depict minimum-energy conformations at the angles $\varphi =0°$, 45°, 90°, and 120°.