Sterol-induced raft-like domains in a model lipid monolayer

A two-dimensional system consisting a mixture of highly coarse-grained saturated (S-type), unsaturated (U-type) lipid molecules, and cholesterol (C-type) molecules is considered to form a model lipid monolayer. All the S-, U-, and C-type particles are spherical in shape, with distinct interaction strengths. The phase behavior of the system is studied for various compositions (x) of the C-type particles, ranging from $x=0.1$ to 0.9. The results show that a structurally ordered complex is formed with the S- and C-types in the fluid-like environment of U-type particles, for $x\in \{0.5-0.6\}$ . The time-averaged hexatic order parameter $\left({\Psi }_6\right)$ indicates that the dynamical segregation of S- and C-types exhibits a positional order that is found to be maximum for x in the range of 0.5 - 0.6. The mean change in the free energy ( $\Delta G\left(x\right)$ ) obtained from the mean change in enthalpy ( $\Delta H$ ) and entropy ( $\Delta S$ ) calculations suggests that $\Delta G$ is minimum for $x\sim 0.6$ . A phenomenological expression for the Gibbs free energy is formulated by explicitly accounting for the individual free energies of S-, U-, and C-type particles and the mutual interactions between them. Minimizing this phenomenological G with respect to the C-type composition results in the optimal value, $x^{\ast }=0.564\pm 0.001$ for stable coexistence of phases; consistent with the simulation results and also the previous experimental observations [1]. All these observations signify the optimal C-type composition, $x\sim 0.5-0.6$ .