Techniques to probe molecular mechanistic events occurring at a single catalytic site of multi-subunit enzymes in real time are few and are still under development. Here time-resolved information is extracted from measurements of the extensive oxygen exchange that occurs at an intermediate stage of adenosine triphosphate (ATP) synthesis during photophosphorylation by chloroplast thylakoids. A stochastic process-based approach for modeling exchange reactions is formulated that provides a physical basis for the kinetic theory. Compatible with the assumptions made in such a model of randomness, the formulation is shown to lead to a Poisson-type theory that enables kinetic analysis of oxygen-exchange data and offers novel physical insights. Parameters such as the apparent rate constant of exchange and the average lifetime of the exchanging intermediates during the synthesis of ATP by the chloroplast F1FO-ATP synthase have been determined over a 5000-fold range of ADP concentration. Experimental isotopomer distributions of [O-18]ATP at high (0.5 mM), intermediate (10 mu M), and low (0.2 mu M) ADP concentrations have been quantified and compared to expected distributions from the theory. The observed distributions are shown to closely match the predicted distributions. A wealth of novel mechanistic insights such as the number of sites/pathways of oxygen exchange, the order of substrate binding steps at the enzyme catalytic site, and regulation of the process of energy coupling have been deduced, and the results are interpreted with the help of available high-resolution X-ray structures. The various biological implications for models of energy coupling have been discussed. Permutation of oxygen ligands about the phosphorus center is proposed as a possible and general but not well-recognized mechanism for oxygen exchange that is consistent with the principal results of this work, and several suggestions for future research are offered.