Derivation of rate equations for multisite ping-pong mechanisms with ping-pong reactions at one or more sites.

It has become clear as the result of the pioneering studies of Northrop on transcarboxylase (l), and the later studies in Lardy’s (2) and Utter’s (3) laboratories on pyruvate carboxylase that biotin-containing enzymes have two-site ping-pong mechanisms in which biotin is carboxylated at one site, and in turn carboxylates a substrate at the second site. The rate equations for such mechanisms have been derived by assuming that the reaction at each site between biotin or carboxybiotin and the other reactants was random sequential. Thus, the conversion of biotin to carboxybiotin at a site was considered proportional to the fractional occupancy of that site by the correct substrates, and to the proportion of the enzyme existing in the form with free biotin at that site. Since the fractional occupancy is given by a simple expression such as: