ABSTRACT The rate acceleration of ATP hydrolysis by F1Fo-ATP synthase is of the order of 1011-fold. We present a cyclic enzyme mechanism for the reaction, relate it to known F1 X-ray structure and speculate on the linkage between enzyme reaction intermediates and subunit rotation. Next, we describe five factors known to be important in the Escherichia coli enzyme for the rate acceleration. First, the provision of substrate binding energy by residues lining the catalytic site is substantial; β-Lys155 and β-Arg182 are specific examples, both of which differentially support substrate MgATP versus product MgADP binding. Second, octahedral coordination of the Mg2+ in MgATP is crucial for both catalysis and catalytic site asymmetry. The residues involved are β-Thr156, β-Glu185 and β-Asp242. Third, there is stabilization of a pentacoordinate phosphorus catalytic transition state by residues β-Lys155, β-Arg182 and α-Arg376. Fourth, residue β-Glu181 binds the substrate water and stabilizes the catalytic transition state. Fifth, there is strong positive catalytic cooperativity, with binding of MgATP at all three sites yielding the maximum rate (Vmax); the molecular basis of this factor remains to be elucidated.