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

TL;DR

The paper presents a highly coarse-grained two-dimensional model of a lipid monolayer composed of saturated (S), unsaturated (U) lipids and cholesterol (C) as spheres with distinct interaction strengths. Through MD simulations and a phenomenological free-energy framework, it identifies an optimal cholesterol fraction around $x \sim 0.6$ that minimizes the Gibbs free energy and maximizes hexatic order, corresponding to raft-like S–C microdomains embedded in a fluid-like U matrix. The study shows that a coupled S–C lattice-like arrangement forms in the $x$ range $0.5 \le x \le 0.6$, with notable enthalpy minimization and enhanced local order, consistent with experimental observations of lipid rafts. These findings provide a tractable, quantitatively-backed picture of raft formation in simplified monolayers and point to future extensions that include molecular orientation to explore $L_o$–$L_d$ transitions in greater depth.

Abstract

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 $x \in \lbrace 0.5 - 0.6\rbrace$. The time-averaged hexatic order parameter $\left\langle Ψ_{6} \right\rangle$ 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 ($ΔG(x)$) obtained from the mean change in enthalpy ($ΔH$) and entropy ($ΔS$) calculations suggests that $ΔG$ 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, $x^* = 0.564 \pm 0.001$ for stable coexistence of phases; consistent with the simulation results and also the previous experimental observations \cite{raghavendra_effect_2023}. All these observations signify the optimal C-type composition, $x \sim 0.5 - 0.6$.

Figures (4)

• Figure 1: (color online) Screenshots of the system at various compositions of C-type, {$x = 0.1, ~0.4, ~0.5, ~0.6, ~0.7 ~~\mathrm{and} ~0.9$}, at density {$\rho^* = 0.1, ~0.3, ~0.5, ~~\mathrm{and} ~0.7$}, and temperature $T^*=0.1$. Yellow, Red, and Blue spheres represent the C, S and U-type particles, respectively.
• Figure 2: (Color online) Change in (a). Enthalpy ($H = U + PV$), (b). Entropy and (c). Free energy averaged over several steady-state configurations, observed relative to their initial values. From the figure we observe that the $\Delta G$ is minimum around $x = 0.6$. (d). Graphical solution to the transcendental equation (\ref{['eq:transcend']}).
• Figure 3: (Color online) Radial distribution function between S and C type particles, $g_{sc}(r)$ observed at the specified values of $x$, indicating maximum number of ordered neighbors when $x$ is in the range of 0.5 to 0.6.
• Figure 4: (Color online) (a),(b). Time variation of the hexatic order parameter observed at every 5th frame of the simulation trajectory written at a frequency of 1000 time units. (c). Time averaged hexatic order parameter at each $x$. Error bars are obtained from the standard deviation of $\psi_{6}(t)$ during its saturated regime.