Looking through a new lens: Expressing the Ping Pong bi bi equation in terms of specificity constants

Abstract

Several biotechnologically important enzymes catalyze reactions by the Ping Pong bi bi mechanism. Traditional kinetic equations for these enzymes contain several terms with combinations of three or four lumped parameters, making it difficult to relate the terms directly to the reaction mechanism. Further, the Ping Pong bi bi reaction mechanism is symmetrical in the forward and reverse directions, but the traditional equations are not mathematically symmetrical. In the present work, we express the Ping Pong bi bi kinetic equation in terms of specificity constants. Our equation is consistent with the traditional equations, but has several conceptual advantages. First, the terms of our equation contain two parameters at most, making it easier to relate the terms to specific features of the reaction mechanism. Second, our equation has only eight lumped parameters, so it has no redundant parameters; traditional equations have nine lumped parameters, such that one is redundant. Third, our equation is mathematically symmetrical, explicitly reflecting the symmetry of the Ping Pong bi bi reaction mechanism. We demonstrate how the parameters of our new equation can be estimated in classic initial rate experiments.