F o F 1 -ATP synthase is the membrane protein catalyzing the synthesis of the 'biological energy currency' adenosine triphosphate (ATP). The enzyme uses internal subunit rotation for the mechanochemical conversion of a proton motive force to the chemical bond. We apply single-molecule Förster resonance energy transfer (FRET) to monitor subunit rotation in the two coupled motors F 1 and F o . Therefore, enzymes have to be isolated from the plasma membranes of Escherichia coli, fluorescently labeled and reconstituted into 120-nm sized lipid vesicles to yield proteoliposomes. These freely diffusing proteoliposomes occasionally traverse the confocal detection volume resulting in a burst of photons. Conformational dynamics of the enzyme are identified by sequential changes of FRET efficiencies within a single photon burst. The observation times can be extended by capturing single proteoliposomes in an anti-Brownian electrokinetic trap (ABELtrap, invented by A. E. Cohen and W. E. Moerner). Here we describe the preparation procedures of F o F 1 -ATP synthase and simulate FRET efficiency trajectories for 'trapped' proteoliposomes. Hidden Markov Models are applied at signal-to-background limits for identifying the dwells and substeps of the rotary enzyme when running at low ATP concentrations, excited by low laser power, and confined by the ABELtrap.