Minimal Lattice Model of Lipid Membranes with Liquid-Ordered Domains

Mixtures of lipids and cholesterol are commonly used as model systems for studying the formation of liquid-ordered ($L_o$) domains in heterogeneous biological membranes. The simplest model system exhibiting coexistence between $L_o$ domains and a liquid-disordered ($L_d$) matrix is that of a binary mixture of saturated lipids like DPPC and cholesterol (Chol). DPPC/Chol mixtures have been investigated for decades both experimentally, theoretically, and recently also by means of atomistic simulations. Here, we present a minimal lattice model that captures the correct behavior of this mixture across multiple scales. On the macroscopic scales, we present simulation results of mixtures of thousands of lipids and Chol molecules which show excellent agreement with the phase diagram of the system. The simulations are conducted on timescales of hundreds of microseconds and show the morphologies and dynamics of the domains. On the molecular scales, the simulations reveal local structures similar to those recently seen in atomistic simulations, including the formation of gel-like nano-domains ($\sim$ 1-10 nm) within larger Chol-rich $L_o$ domains ($\sim$ 10-100 nm). The observed multi-scale behavior is related to the tendency of Chol to induce ordering of acyl chains on the one hand, and disrupt their packing with each other, on the other hand.