F1Fo-ATP synthase is the enzyme responsible for most of the ATP synthesis in living systems. The catalytic domain F 1 of the F1Fo complex, F1-ATPase, has the ability to hydrolyze ATP. A fundamental problem in the development of a detailed mechanism for this enzyme is that it has not been possible to determine experimentally the relation between the ligand binding affinities measured in solution and the different conformations of the catalytic  subunits (TP, DP, E) observed in the crystal structures of the mitochondrial enzyme, MF 1. Using free energy difference simulations for the hydrolysis reaction ATP؉H 2O 3 ADP؉Pi in the TP and DP sites and unisite hydrolysis data, we are able to identify TP as the ''tight'' (K D ؍ 10 ؊12 M, MF1) binding site for ATP and DP as the ''loose'' site. An energy decomposition analysis demonstrates how certain residues, some of which have been shown to be important in catalysis, modulate the free energy of the hydrolysis reaction in the TP and DP sites, even though their structures are very similar. Combined with the recently published simulations of the rotation cycle of F 1-ATPase, the present results make possible a consistent description of the binding change mechanism of F 1-ATPase at an atomic level of detail. T he enzyme F 1 F o -ATP synthase is responsible for most of the ATP synthesis in living systems (1-3). It is a large multisubunit complex consisting of a proton-translocating membrane domain F o attached via central and peripheral stalks to the catalytic domain F 1 , a spherical globular structure outside of the membrane (4-6). The F 1 domain, called F 1 -ATPase, is made up of 3␣ and 3 subunits arranged in alternation around the ␣-helical coiled-coil structure of the ␥ subunit. The foot of the ␥ subunit is a more globular domain and makes extensive contacts with the ring of c subunits of the membrane portion, F 0 (7). The ␥ subunit and the associated c ring are believed to rotate as an ensemble relative to the rest of the enzyme, the rotation being generated by the transmembrane proton-motive force via photosynthesis or respiration. The ␣-helical domain of the ␥ subunit is asymmetric and the rotation of this asymmetrical structure alters the conformations (4-6) and the binding affinities (8, 9) of the three catalytic  subunits for substrate and products. Each of them in turn is thought to go through three states known as open, loose, and tight (4), in accord with the ''binding change'' mechanism of ATP synthesis (1). The F 1 domain can be separated from the membrane domain and it retains the ability to hydrolyze ATP. Hydrolysis of ATP leads to the rotation of the central stalk, although the detailed mechanism is not understood. By attaching an actin filament or a bead to the exposed foot of the central stalk, the rotation has been visualized in a microscope (10). The actin filament turns counterclockwise (as viewed from the membrane) in 120°steps. During the ATP synthesis cycle, the rotation of the central stalk is presumed to be in the opposite sense.Of...