  FoF1-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 F\"orster resonance energy
transfer (FRET) to monitor subunit rotation in the two coupled motors F1 and
Fo. 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 FoF1-ATP synthase and simulate FRET
efficiency trajectories for 'trapped' proteoliposomes. Hidden Markov Models are
applied at signal-to-background ratio 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.
