MesoMem: A mesoscale membrane model based on an additive potential

TL;DR

A new, solvent-free, one-particle-thick, coarse-grained model for lipid bilayers, governed by an additive potential, that accurately reproduces the theoretical fluctuation spectrum for tensionless membranes and exhibits tunable mechanical properties, including biologically relevant bending rigidities and area compressibility moduli is introduced.

Abstract

Bridging the gap between atomistic detail and continuum mechanics is a central challenge in modeling biological membranes, particularly for mesoscopic phenomena spanning large length and time scales. In this work, we introduce a new, solvent-free, one-particle-thick, coarse-grained model for lipid bilayers, governed by an additive potential. Our approach treats orientational elasticity through distinct additive energy terms for tilt and splay, offering an unbiased potential form. The model is implemented in the LAMMPS molecular dynamics engine. Our simulations show spontaneous self-assembly of lamellar structures and stable vesicles from disordered states. We map the dynamical phase diagram of the system, identifying distinct gel-like, fluid, and gas regimes, controlled by temperature and the steepness of the isotropic attraction. The model accurately reproduces the theoretical $1/q^{4}$ fluctuation spectrum for tensionless membranes and exhibits tunable mechanical properties, including biologically relevant bending rigidities and area compressibility moduli. We show how we can include osmotic pressure and spontaneous curvature in our model. Finally, we demonstrate the model's applicability to complex membrane remodeling by simulating the adhesive wrapping of colloidal nanoparticles, recovering the predicted dependency on particle size and adhesion strength.

Figures (17)

• Figure 1: Schematic of the model and interaction geometry. (A) Representation of a lipid bilayer patch as a single coarse-grained particle. The particle has rotational symmetry. (B) The separation vector $\vec{r}_{ij}$, and normal vectors $\hat{n}_i$ and $\hat{n}_j$ used in the derivation of the potential. (C) Schematic illustrating the forces resulting from a tilt deformation. (D) Schematic illustrating the torques resulting from a splay deformation.
• Figure 2: Isotropic potential $U(r)$ with isotropic cutoff $r_{\text{c}}=3.0$. The $\zeta$ parameter is tuning the slope of the attractive branch of the potential.
• Figure 3: Overview of simulated lipid systems. (A) Self-assembled patches formed from 1500 randomly placed particles. (B) Planar membrane colored according to $z$-height. (C) Lipid vesicle composed of zero spontaneous curvature beads (in red) and non-zero spontaneous curvature $C_0 = 0.1 \sigma^{-1}$ beads (in blue). (D) Spherical vesicle shown as an $xz$-cross-section (top) and whole vesicle (bottom). (E) Membrane tube. (F) Cross-section ($xz$-plane) of a spherical vesicle wrapping a particle. (G) Planar membrane interacting with multiple soft colloidal metaparticles paesaniMetaparticlesComputationallyEngineered2024. Initial configurations have been generated following the procedures described in Sec. \ref{['init']} of the Supplementary Material.
• Figure 4: Dynamical phase diagram of the membrane model in the ($T$, $\zeta$) parameter space. The color map represents the scaling exponent $\alpha$ obtained from the power-law fit of the lipid Mean Squared Displacement ($\text{MSD} \propto t^\alpha$). We indentify three distinct regimes: a sub-diffusive solid/gel phase ($\alpha \ll 1$), a diffusive fluid phase ($\alpha \approx 1$), and a super-diffusive gas-like regime ($\alpha \gg 1$) corresponding to membrane disintegration. Fixed model parameters: $N=2500$, $k_{\text{tilt}}=12$, $k_{\text{splay}}=12$, $w_{\text{c}}=1.7\sigma$ and $r_{\text{c}}=2.5 \sigma$.
• Figure 5: Lateral diffusion coefficient $D$ of membrane lipids as a function of temperature $T$ and interaction parameter $\zeta$, from the same simulations as used for Fig. \ref{['fig:phase_plot']}. $D$ was calculated by fitting the MSD to $\text{MSD} = 4Dt$ in the linear regime. Points of the dataset corresponding to a system in the gas phase have been excluded from the plot. Errorbars are standard deviations over 3 independent replicas.