ATP synthase is an enzyme, a molecular motor, and an ion channel all wrapped together in one structure (Fig. 1). It is an enzyme, because it generates ATP. It is a molecular motor, because the central rotor part turns about 150 times every second during ATP synthesis (Source: MRC mitochondrial Biology Unit). It is an ion channel, because it funnels protons into the mitochondrion during ATP generation (Source: Davidson College).
ATP synthase. Source: Ace Biochemistry
ATP synthase is composed of two subunits, F0 and F1. The 0 subunit is embedded in the inner membrane, and the other, containing the catalytic parts, protrudes into the matrix.
F0 contains the proton channel and is connected to F1 with a stalk.
F1 consists of five polypeptide chains, alpha (a), beta (b), gamma (g), delta (d), and epsilon (e). The alpha and beta chains make up the bulk of F1 and are arranged in a hexameric ring. Both chains bind nucleotides, but only beta participates in catalysis (Source: ACE Biochemistry).
Another example of complex proteins are G-protein coupled receptors, for example those linked to ion channels (Fig. 2).
G protein coupled receptors. Image source: Wikipedia
Here, a receptor is bound to a G-protein, that becomes activated after receptor binding. The G protein then leaves the receptor and travels to an ion channel and activates it (or inhibits it).