  FoF1-ATP synthases are ubiquitous membrane-bound, rotary motor enzymes that
can catalyze ATP synthesis and hydrolysis. Their enzyme kinetics are controlled
by internal subunit rotation, by substrate and product concentrations, by
mechanical inhibitory mechanisms, but also by the electrochemical potential of
protons across the membrane. Single-molecule F\"orster resonance energy
transfer (smFRET) has been used to detect subunit rotation within FoF1-ATP
synthases embedded in freely diffusing liposomes. We now report that kinetic
monitoring of functional rotation can be prolonged from milliseconds to seconds
by utilizing an Anti-Brownian electrokinetic trap (ABEL trap). These extended
observation times allowed us to observe fluctuating rates of functional
rotation for individual FoF1-liposomes in solution. Broad distributions of
ATP-dependent catalytic rates were revealed. The buildup of an electrochemical
potential of protons was confirmed to limit the maximum rate of ATP hydrolysis.
In the presence of ionophores or uncouplers, the fastest subunit rotation
speeds measured in single reconstituted FoF1-ATP synthases were 180 full rounds
per second. This was much faster than measured by biochemical ensemble
averaging, but not as fast as the maximum rotational speed reported previously
for isolated single F1 complexes uncoupled from the membrane-embedded Fo
complex. Further application of ABEL trap measurements should help resolve the
mechanistic causes of such fluctuating rates of subunit rotation.
