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 accurately reproduce 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 small gel-like nano-domains within larger Chol-rich $L_o$ domains. The observed multi-scale behavior is fully explained in terms of (i) a competition between the packing enthalpy and configurational entropy of the lipid chains, and (ii) the "dual effect" of the Chol on the membrane fluidity.