Mechanism equivalence in enzyme-substrate reactions: Distributed differential delay in enzyme kinetics

We consider single enzyme-substrate reaction mechanisms involving multiple complexes and demonstrate that these are equivalent to a distributed delay system without complexes. The distribution of the delay is determined by the number of intermediates and the relative sizes of the rates of the individual reaction mechanisms. We also consider the limit where there are a large number of intermediate complexes, and the conditions under which a number of known reaction mechanisms are equivalent. The present formalism brings forth new perspectives in the implementation of experimental techniques to rule out particular reaction mechanisms by studying the distribution of the delay between reactant mixing and product formation.