A theoretical analysis of the crossover theorem is presented based on a linear approximation. Cases are considered in which the simple crossover theorem may lead to erroneus conclusions. Among them are the following: more than one interaction site of an effector with the enzymatic chain; influx and efflux of metabolites regulated by outer metabolic processes; existence of inner effectors; conservation equations for metabolite concentrations; and changes of the state of complexes with the metabolites. It is shown that the action of an effector does not always produce a crossover at the affected enzyme. On the other hand, examples are given where “pseudo-crossovers” occur at unaffected enzymes. It is concluded that for real systems the identification of the interaction sites of an effector with an enzymatic chain cannot be achieved by the simple crossover theorem. Furthermore, even the identification of “rate controlling” or “regulatory important” enzymes by means of crossovers must be done with great caution.
A simple and general procedure for the identification of interaction sites of an outer effector with an enzymatic chain is proposed. It requires the determination of the flux through the chain, the concentrations of the substrates and products of the enzymatic step under consideration and the rate law by which an inner effector, if present, influences the reaction rate of this step.