  In an effort to understand ``rafts'' in biological membranes, we propose
phenomenological models for saturated and unsaturated lipid mixtures, and
lipid-cholesterol mixtures. We consider simple couplings between the local
composition and internal membrane structure, and their influence on transitions
between liquid and ``gel'' membrane phases. Assuming that the gel transition
temperature of the saturated lipid is shifted by the presence of the
unsaturated lipid, and that cholesterol acts as an external field on the chain
melting transition, a variety of phase diagrams are obtained. The phase
diagrams for binary mixtures of saturated/unsaturated lipids and
lipid/cholesterol are in semi-quantitative agreement with the experiments. Our
results also apply to regions in the ternary phase diagram of
lipid/lipid/cholesterol systems.
