  FoF1-ATP synthases are the ubiquitous membrane enzymes which catalyze ATP
synthesis or ATP hydrolysis in reverse, respectively. 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. By utilizing an
Anti-Brownian electrokinetic trap (ABEL trap), single-molecule F\"orster
resonance energy transfer (smFRET)-based subunit rotation monitoring was
prolonged from milliseconds to seconds. The extended observation times for
single proteoliposomes in solution allowed to observe fluctuating rotation
rates of individual enzymes and to map the broad distributions of ATP-dependent
calatytic rates in FoF1-ATP synthase. The buildup of an electrochemical
potential of protons was confirmed to limit the maximum rate of ATP hydrolysis.
In the presence of ionophores and uncouplers the fastest subunit rotation
speeds measured in single reconstituted FoF1-ATP synthases were 180 full rounds
per second, i.e. much faster than measured by biochemical ensemble averaging,
but not as fast as the maximum rotational speed reported previoulsy for
isolated single F1 fragments without coupling to the membrane-embedded Fo
domain of the enzyme.
