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The Michaelis-Menten enzymatic reaction is sufficient to perceive manysubtleties of network modeling, including the concentration and time scalesseparations, the formal equivalence between bulk phase and single-moleculeapproaches, or the relationships between single-cycle transient probabilitiesand steady state rates. Seven methods proposed by different authors andyielding the same famous Michaelis-Menten equation, are selected here toillustrate the kinetic and probabilistic use of rate constants and to reviewbasic techniques for handling them. Finally, the general rate of an orderedmultistep reaction, of which the Michaelis-Menten reaction is a particularcase, is deduced from a Markovian approach.

Seven competing ways to recover the Michaelis-Menten equation reveal the alternative approaches to steady state modeling