Transient phase of enzyme reactions.: Time course equations of the strict and the rapid equilibrium conditions and their computerized derivation

In this contribution, we present the derivation, from the strict transient phase equations of enzyme reactions, of the transient phase equations under the usual assumptions that one or more of the reversible steps involved in the mechanism of the enzyme reaction are assumed to be in rapid equilibrium. Moreover, we present the transient phase equations of all of the species in a general enzyme system model, valid for the partial or total rapid equilibrium conditions, as well as the particular case of the strict transient phase equations. In the case of the rapid equilibrium assumptions, the equations may be given either as functions of the individual rate constants in the reversible steps assumed in rapid equilibrium or as functions of the corresponding equilibrium constants. The steady state equations are easily obtained from the transient phase equations by setting the time →∞. We have implemented a computer program, easy to use and with a user-friendly format for the input of data and output of results, which allows the user to derive the symbolic strict transient phase equations and/or those corresponding to the assumption that one or more of the reversible reaction steps are in rapid equilibrium.