  We use a lattice model of a ternary mixture containing saturated and
unsaturated lipids with cholesterol (Chol), to study the structural properties
characterizing the coexistence between the liquid-disordered and liquid-ordered
phases. Depending on the affinity of the saturated and unsaturated lipids, the
system may exhibit macroscopic (thermodynamic) liquid-liquid phase separation,
or be divided into small-size liquid-ordered domains surrounded by a
liquid-disordered matrix. In both cases, it is found that the nano-scale
structure of the liquid-ordered regions is heterogeneous, and that they are
partitioned into Chol-rich sub-domains and Chol-free, gel-like, nano-clusters.
This emerges as a characteristic feature of the liquid-ordered state, which
helps distinguishing between liquid-ordered domains in a two-phase mixture, and
similar-looking domains in a one-phase mixture that are rich in saturated
lipids and Chol, but are merely thermal density fluctuations. The
nano-structure heterogeneity of the liquid-ordered phase can be detected by
suitable experimental spectroscopic methods, and is observed also in atomistic
computer simulations.
