One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes

Biological membranes are involved in numerous intriguing biophysical and biological cellular phenomena of different length scales, ranging from nanoscale raft formation, vesiculation, to microscale shape transformations. With extended length and time scales as compared to atomistic simulations, solvent-free coarse-grained membrane models have been exploited in mesoscopic membrane simulations. In this study, we present a one-particle-thick fluid membrane model, where each particle represents a cluster of lipid molecules. The model features an anisotropic interparticle pair potential with the interaction strength weighed by the relative particle orientations. With the anisotropic pair potential, particles can robustly self-assemble into fluid membranes with experimentally relevant bending rigidity. Despite its simple mathematical form, the model is highly tunable. Three potential parameters separately and effectively control diffusivity, bending rigidity, and spontaneous curvature of the model membrane. As demonstrated by selected examples, our model can naturally simulate dynamics of phase separation in multicomponent membranes and the topological change of fluid vesicles.

Figure 1

(Color online) Schematics of the orientation-dependent interparticle interaction. Kinetically, each particle is axisymmetric with a particle-fixed unit vector $\mathbf{n}$ representing the axis of symmetry, and with mass of $m$. The interparticle interaction is both distance and orientation dependent. The angle ${\theta }_0$ is a model parameter charactering the spontaneous curvature. The configuration corresponding to ${\theta }_i={\theta }_j={\theta }_0$ is made to be the most energetically favorable relative orientation between two particles. The two halves of each particle are colored distinctly to indicate the orientation of the particle. The spontaneous curvature $c_0$ is related to ${\theta }_0$ via $c_0\sim 2\text{sin}{\theta }_0/d_0$, where $d_0$ is the average interparticle distance.

Figure 2

(Color online) (a) The slope of the attractive branch of the distance-dependent function varies with the exponent $\zeta$. The solid black curve represents the repulsive branch of the function. (b) The interparticle potential $U$ as a function of $r$ for three different ${\theta }_i$ $\left({\theta }_j={\theta }_i\right)$ with $\zeta =4$, $\mu =3$, and ${\theta }_0=0$. The double arrows denote the orientations of a particle pair.

Figure 3

(Color online) Snapshots from CGMD simulations demonstrating self-assembly of randomly distributed particles into vesicles. The parameters used in the simulations are $\zeta =4$, $\mu =3$, ${\theta }_0=0$, and $k_{\text{B}}T=0.17\epsilon$.

Figure 4

(Color online) Phase diagram in the $\left(\zeta ,T\right)$ plane at zero tension. Three regions representing gel, fluid, and gas phases are identified, separated by solid lines. A broad fluid phase region with diffusion constant on the order of $0.1{\sigma }^2/\tau$ exists.

Figure 5

(Color online) Diffusion constant $D$ and interparticle distance $d$ as functions of the exponent $\zeta \left(k_{\text{B}}T=0.2\epsilon \right)$ (a) and temperature (b) for tensionless membranes. The thermal expansion coefficient ${\alpha }_T$ of the membrane at different temperature ranges is fitted and indicated in (b).

Figure 6

(Color online) Membrane tension as a function of area strain $\Delta A/L^2$. Area compression modulus $K_A$ is fitted to be about $18k_{\text{B}}T/{\sigma }^2$. The parameters used in the simulations are $\zeta =4$, $\mu =3$, ${\theta }_0=0$, and $k_{\text{B}}T=0.23\epsilon$.

Figure 7

(Color online) (a) Fluctuation spectra under zero and finite tensions for planar membranes. Both $q^{-4}$ and $q^{-2}$ dependences are well predicted in simulations. The parameters used in the simulations are $\zeta =4$, $\mu =3$, ${\theta }_0=0$, and $k_{\text{B}}T=0.23\epsilon$. (b) Membrane bending rigidity (in zero-tension states) monotonically increases with $\mu$, while the order of alignment of the axis of symmetry of particles monotonically decreases with $\mu$. The parameters used in the simulations are $\zeta =4$, ${\theta }_0=0$, and $k_{\text{B}}T=0.23\epsilon$.

Figure 8

(Color online) Spontaneous curvature mediated phase separation and subsequent budding.

Figure 9

(Color online) Simulation snapshots of nanoparticle endocytosis.