Coarse-grained molecular dynamics simulation of binary charged lipid membranes: Phase separation and morphological dynamics

Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover, the electrostatic repulsion causes morphological changes, such as pore formation, and further transformations into disk, string, and bicelle structures, which are spatiotemporally coupled to the lateral segregation of charged lipids. Based on our coarse-grained MD simulation, we propose a plausible mechanism of pore formation at the molecular level. The pore formation in a charged-lipid-rich domain is initiated by the prior disturbance of the local molecular orientation in the domain.

Figure 1

(a) Typical snapshots of the lateral phase separation of a neutral vesicle consisting of 2500 neutral A-lipids [head, red (dark); tail, green] and 2500 neutral B-lipids [head, yellow (light); tail, cyan]. After rapid relaxation on the order of $t\sim 0.1\times 7500\tau$, the binary vesicle reaches a quasiequilibrium state. Attractive interaction parameters are set to $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =1.7,w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$, and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$. (b) Time evolution of the attractive potential $V_{\mathrm{attr}}$ per lipid molecule during the lateral phase separation for $t=1.0\times 7500\tau$ under various attractive interactions between A-lipids of $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =1.6$, 1.65, 1.7, 1.75, and 1.8. Calculations were performed five times for each $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$ value to ensure reproducibility.

Figure 2

(a) Mean-squared diffusion length of a lipid in $1000dt$ plotted vs attractive interaction parameter $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$. (b) Nematic order parameter $S$ plotted vs $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$. The values are averaged spatially over a vesicle and temporally over $\left(0.9\text{–}1.0\right)\times 7500\tau$ for each $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$ in both (a) and (b). Error bars represent the standard deviations. Other interaction parameters are set to $w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$ and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$.

Figure 3

(a) Typical snapshots of the lateral phase separation of a charged vesicle consisting of 2500 charged A-lipids [head, red (dark); tail, green] and 2500 neutral B-lipids [head, yellow (light); tail, cyan] at salt concentrations $n_0=1\mathrm{M}$ and $100\mathrm{mM}$. Attractive interaction parameters are set to $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =1.7,w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$, and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$ for both salt conditions. (b) Attractive and (c) electrostatic repulsive potentials $V_{\mathrm{attr}}$ and $V_{\mathrm{elec}}$, respectively, for $t=1.0\times 7500\tau$ under various attractive interactions between A-lipids of $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =1.6$, 1.65, 1.7, 1.75, and 1.8 at $n_0=1\mathrm{M}$. (d) Attractive and (e) electrostatic repulsive potentials at $n_0=100\mathrm{mM}$. Calculations were performed three times for each $n_0$ and $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$ value to ensure reproducibility.

Figure 4

(a) Typical snapshots of the lateral phase separation of neutral (upper) and charged (at $n_0=100\mathrm{mM}$, lower) vesicles for $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$, 1.525, 1.55, 1.575, and 1.6. Other conditions are set to $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$, A:B = 2500:2500. (b) Corresponding attractive potentials $V_{\mathrm{attr}}$. Calculations were performed three times for each charge condition and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma$ value to ensure reproducibility.

Figure 5

Density correlation functions between lipid species. The intersection between the (A-A) correlation curve and (A-B) correlation curve is the typical domain size of A-lipid-rich domains. Typical conditions, where $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7,w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$, A:B=1500:3500, and $t=1.0\times 7500\tau$, are used as an example.

Figure 6

(a) Time evolution of domain size for neutral vesicles consisting of neutral A- and B-lipids (black filled circles) and charged vesicles consisting of charged A-lipids and neutral B-lipids at $n_0=1\mathrm{M}$ (purple filled squares) and $n_0=100\mathrm{mM}$ (red open squares). Lipid composition of A:B = 2500:2500. Error bars represent the standard deviation at each time. Calculations were performed five times for neutral and charged lipids at $n_0=1\mathrm{M}$, and three times for charged lipids at $n_0=100\mathrm{mM}$. Slopes for $t^{0.5}$ and $t^{0.333}$ in the double logarithmic axis are shown as visual guides. (b) Lipid composition of A:B = 1500:3500 in the same manner in (a). Calculations were performed twenty times for neutral, and ten times for charged lipids at $n_0=1\mathrm{M}$ and $100\mathrm{mM}$. Slopes for $t^{0.5},t^{0.4}$, and $t^{0.333}$ are shown as visual guides.

Figure 7

(a) Typical snapshots of the morphological changes of a binary charged vesicle composed of 2500 charged A-lipids [head, red (dark); tail, green] and 2500 neutral B-lipids [head, yellow (light); tail, cyan] at $n_0=100\mathrm{mM}$. $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =1.75,w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$, and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$. The upper and lower image series, respectively, show surface and cross-sectional images of the same vesicle. Typically, the morphological changes occur an order of magnitude slower $\left(t\sim 1.0\times 7500\tau \right)$ than the lateral phase separation $\left(t\sim 0.1\times 7500\tau \right)$. Time evolution of the (b) attractive and (c) electrostatic repulsive potentials $V_{\mathrm{attr}}$ and $V_{\mathrm{elec}}$ per lipid molecule, respectively. The calculation was performed once and showed plausible results (see Fig. 8).

Figure 8

(a) Typical morphologies for various salt conditions and attractive interactions between A-lipids. $n_0$ is from $10\mathrm{mM}$ to $1\mathrm{M}$ and $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma$ is from 1.6 to 1.8. $w_{\mathrm{c}}^{\mathrm{BB}}/\sigma$ and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma$ were fixed as 1.7 and 1.5, respectively. (b) Phase diagram of the charged vesicle morphologies. We defined four types of morphologies; spherical vesicle (circle), disk (square), string (triangle), and bicelle (cross). The dashed lines are visual guides indicating the phase boundaries.

Figure 9

Example of the molecular mechanism of pore formation. The vesicle is composed of 2500 charged A-lipids [head, red (dark); tail, green] and 2500 neutral B-lipids [head, yellow (light); tail, cyan] at $n_0=100\mathrm{mM}$. $w_{\mathrm{c}}^{\mathrm{AA}}/\sigma =w_{\mathrm{c}}^{\mathrm{BB}}/\sigma =1.7$ and $w_{\mathrm{c}}^{\mathrm{AB}}/\sigma =1.5$. Sequential snapshots in the middle show the surface and cross-sectional images taken at $t=7.0\times 7500\tau$ to $9.8\times 7500\tau$. Dotted squares contain magnified images of the pore-forming site at $t=7.4\times 7500\tau$ (before), $7.8\times 7500\tau$ (onset), and $8.2\times 7500\tau$ (after), for surface (upper) and cross-sectional (lower) views of the bilayer membrane. Embedded lipids and the surrounding lipids are displayed with spheres of the original size and small spheres, respectively.