Coarse-grained molecular dynamics simulation for uptake of nanoparticles into a charged lipid vesicle dominated by electrostatic interactions

We use a coarse-grained molecular dynamics simulation to investigate the interaction between neutral or charged nanoparticles (NPs) and a vesicle consisting of neutral and negatively charged lipids. We focus on the interaction strengths of hydrophilic and hydrophobic attraction and electrostatic interactions between a lipid molecule and an NP. A neutral NP passes through the lipid membrane when the hydrophobic interaction is sufficiently strong. As the valence of the positively charged NP increases, the membrane permeation speed of the NP is increased compared with the neutral NP and charged lipids are accumulated around the charged NP. A charged NP with a high valence passes through the lipid membrane via a transient channel formed by charged lipids or transportlike endocytosis. These permeation processes can be classified based on analyses of the density correlation function. When the nonelectrostatic interaction parameters are large enough, a negatively charged NP can be adsorbed on the membrane and a neutral lipid-rich region is formed directly below the NP. The NP is spontaneously incorporated into the vesicle under various conditions and the incorporation is mediated by the membrane curvature. We reveal how the NP's behavior depends on the NP valence, size, and the nonelectrostatic interaction parameters.

Figure 1

(a) Typical snapshots of the permeation sequence of a neutral NP ($z_{\mathrm{n}}=0$) for $d/\sigma =5,v_{\mathrm{nh}}/k_{\mathrm{B}}T=2$, and $v_{\mathrm{nt}}/k_{\mathrm{B}}T=3$. Charged lipid (A-lipid) is represented by red (dark in grayscale) hydrophilic beads and green hydrophobic beads, while neutral lipid (B-lipid) is represented by yellow (light in grayscale) hydrophilic beads and cyan hydrophobic beads. (b) Time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$, for $t=1\times 7500\tau$. (c) Enlarged graph for time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$ until $t=0.1\times 7500\tau$. (d) Time evolution of the electrostatic interaction between lipids, $V_{\mathrm{el}}^{\left(\mathrm{LL}\right)}$, for $t=1\times 7500\tau$. [(e) and (f)] Density correlation functions of lipids and beads around the NP at $t=0.07\times 7500\tau$, respectively. Red and blue lines in (e) indicate the density correlation functions of A- and B-lipids, respectively. Red, blue, and green lines in (f) indicate the density correlation functions of the a-, b-, and c-beads, respectively. [(g) and (h)] Density correlation functions of A- and B-lipids in the inner leaflet in (g) and outer leaflet in (h) around the NP at $t=1\times 7500\tau$. Red and blue lines indicate the density correlation functions of A- and B-lipids, respectively.

Figure 2

[(a) and (b)] Summary of neutral NP behavior at $t=1\times 7500\tau$ for $d/\sigma =5$ and 2, respectively. Open circles, gray squares, filled triangles, and the cross indicate adsorption on the outer leaflet, adsorption on the inner leaflet, localization in the hydrophobic core, and desorption from the outer leaflet, respectively. Dashed lines roughly indicate the boundaries of the behaviors. Schematic illustration of NP behavior is shown in a square box. (c) Typical snapshots of NP behavior.

Figure 3

(a) Typical snapshots of the permeation sequence of a charged NP ($z_{\mathrm{n}}=+50$) for $d/\sigma =5,v_{\mathrm{nh}}/k_{\mathrm{B}}T=2$, and $v_{\mathrm{nt}}/k_{\mathrm{B}}T=3$. Charged lipid (A-lipid) is represented by red (dark in grayscale) hydrophilic beads and green hydrophobic beads, while neutral lipid (B-lipid) is represented by yellow (light in grayscale) hydrophilic beads and cyan hydrophobic beads. (b) Time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$ (black line), and the electrostatic interaction between the NP and lipids, $V_{\mathrm{el}}^{\left(\mathrm{NL}\right)}$ (red line), for $t=1\times 7500\tau$. (c) Time evolution of the electrostatic interaction between lipids $V_{\mathrm{el}}^{\left(\mathrm{LL}\right)}$ for $t=1\times 7500\tau$. [(d) and (e)] Density correlation functions of lipids and beads around the NP at $t=0.02\times 7500\tau$, respectively. Red and blue lines in (d) indicate the density correlation functions of A- and B-lipids, respectively. Red, blue, and green lines in (e) indicate the density correlation functions of a-, b-, and c-beads, respectively. [(f) and (g)] Density correlation functions of A- and B-lipids in the inner leaflet in (f) and outer leaflet in (g) around the NP at $t=1\times 7500\tau$. Red and blue lines indicate the density correlation functions of A- and B-lipids, respectively. (h) Snapshots at $t=1\times 7500\tau$. [(i) and (j)] Lipid distribution changes in inner and outer leaflets as functions of distance and time, respectively. Color represents lipid distribution, and positive and negative values indicate charged lipid (A-lipid)-rich region and neutral lipid (B-lipid)-rich region, respectively.

Figure 4

(a) Typical snapshots of the permeation sequence of a charged NP ($z_{\mathrm{n}}=+150$) through a transient channel for $d/\sigma =5,v_{\mathrm{nh}}/k_{\mathrm{B}}T=2$, and $v_{\mathrm{nt}}/k_{\mathrm{B}}T=3$. Charged lipid (A-lipid) is represented by red (dark in grayscale) hydrophilic beads and green hydrophobic beads, while neutral lipid (B-lipid) is represented by yellow (light in grayscale) hydrophilic beads and cyan hydrophobic beads. (b) Time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$, for $t=1\times 7500\tau$. (c) Time evolution of the electrostatic interaction between the NP and lipids, $V_{\mathrm{el}}^{\left(\mathrm{NL}\right)}$, for $t=1\times 7500\tau$. [(d) and (e)] Density correlation functions of lipids and beads around the NP at $t=0.03\times 7500\tau$, respectively. Red and blue lines in (d) indicate the density correlation functions of the A- and B-lipids, respectively. Red, blue, and green lines in (e) indicate the density correlation functions of the a-, b-, and c-beads, respectively.

Figure 5

(a) Typical snapshots of the permeation sequence of a charged NP ($z_{\mathrm{n}}=+200$) via transportlike endocytosis when $d/\sigma =5,v_{\mathrm{nh}}/k_{\mathrm{B}}T=2$, and $v_{\mathrm{nt}}/k_{\mathrm{B}}T=3$. Charged lipid (A-lipid) is represented by red (dark in grayscale) hydrophilic beads and green hydrophobic beads, while neutral lipid (B-lipid) is represented by yellow (light in grayscale) hydrophilic beads and cyan hydrophobic beads. (b) Time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$, for $t=1\times 7500\tau$. (c) Time evolution of the electrostatic interaction between the NP and lipids, $V_{\mathrm{el}}^{\left(\mathrm{NL}\right)}$, for $t=1\times 7500\tau$. [(d) and (e)] Density correlation functions of lipids and beads around the NP at $t=0.1\times 7500\tau$, respectively. Red and blue lines in (d) indicate the density correlation functions of A- and B-lipids, respectively. Red, blue, and green lines in (e) indicate the density correlation functions of a-, b-, and c-beads, respectively.

Figure 6

(a) Typical snapshots of a negatively charged NP ($z_{\mathrm{n}}=-50$) when $d/\sigma =5,v_{\mathrm{nh}}/k_{\mathrm{B}}T=2$, and $v_{\mathrm{nt}}/k_{\mathrm{B}}T=3$. Charged lipid (A-lipid) is represented by red (dark in grayscale) hydrophilic beads and green hydrophobic beads, while neutral lipid (B-lipid) is represented by yellow (light in grayscale) hydrophilic beads and cyan hydrophobic beads. (b) Time evolution of the Lennard-Jones potential between the NP and lipids, $V_{\mathrm{LJ}}^{\left(\mathrm{NL}\right)}$ (black line), and the electrostatic interaction between the NP and lipids, $V_{\mathrm{el}}^{\left(\mathrm{NL}\right)}$ (red line), for $t=1\times 7500\tau$. (c) Time evolution of the electrostatic interaction between lipids, $V_{\mathrm{el}}^{\left(\mathrm{LL}\right)}$, for $t=1\times 7500\tau$. [(d) and (e)] Density correlation functions of lipids and beads around the NP at $t=1\times 7500\tau$, respectively. Red and blue lines in (d) indicate the density correlations functions of A- and B-lipids, respectively. Red, blue, and green lines in (e) indicate the density correlation functions of a-, b-, and c-beads, respectively. [(f) and (g)] Density correlation functions of A- and B-lipids in the inner leaflet in (f) and outer leaflet in (g) around the NP at $t=0.14\times 7500\tau$. Red and blue lines indicate the density correlation functions of A- and B-lipids, respectively. (h) Snapshots at $t=0.14\times 7500\tau$. [(i) and (j)] Lipid distribution changes in inner and outer leaflets as functions of distance and time, respectively. Color represents lipid distribution, and positive and negative values indicate charged lipid (A-lipid)-rich region and neutral lipid (B-lipid)-rich region, respectively.

Figure 7

Summary of charged NP behavior at $t=1\times 7500\tau$ and uptake dynamics. The valences and the diameters of NPs ($z_{\mathrm{n}},d/\sigma$) are (a) ($+10$, 5), (b) ($+50$, 5), (c) ($+150$, 5), (d) ($+200$, 5), (e) ($-50$, 5), (f) ($+10$, 2), (g) ($+50$, 2), (h) ($+150$, 2), (i) ($+200$, 2), and (j) ($-50$, 2). Open circles, squares (gray, red, and blue), filled triangles, and crosses indicate adsorption onto the outer leaflet, adsorption onto the inner leaflet, localization in the hydrophobic core, and desorption from the outer leaflet, respectively. Gray, red, and blue squares indicate permeation through the hydrophobic core, through the transient channel, and by transportlike endocytosis, respectively. Dashed lines roughly indicate the boundaries of the behaviors. Schematic and typical snapshot of the NP behaviors are shown at the bottom of the figure.