  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 show excellent
agreement with 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 gel-like nano-domains ($\sim$ 1-10 nm) within larger Chol-rich
$L_o$ domains ($\sim$ 10-100 nm). The observed multi-scale behavior is related
to the tendency of Chol to induce ordering of acyl chains on the one hand, and
disrupt their packing with each other, on the other hand.
