Phase separation in three-component lipid membranes: from Monte Carlo simulations to Ginzburg-Landau equations.

Preferential affinity of cholesterol for saturated rather than unsaturated lipids underlies the thermodynamic process of the formation of lipid nanostructures in cell membranes, that is, of rafts. In this context, phase segregation of two-dimensional ternary lipid mixtures is formally studied from two different perspectives. The simplest approach is based on Monte Carlo simulations of an Ising model corresponding to two interconnected lattices, from which the basic features of the phenomenon are investigated. Then, the coarse-graining mean field procedure of the discrete Hamiltonian is adapted and a Ginzburg-Landau-like free energy expression is obtained. From this latter description, we construct kinetic equations that enable us to perform numerical simulations and to establish analytical phase separation criteria. Application of our formalism in the biological context is also discussed.