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

Denis Michel (1) , Philippe Ruelle (2)

1 Trec - Transcription, environnement et cancer
2 UCL IRMP - Institut de Recherche en Mathématiques et Physique

The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Twelve methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and probabilistic use of rate constants and to review basic techniques for handling them. Finally, the general rate of an ordered multistep reaction, of which the Michaelis-Menten reaction is a particular case, is deduced from a Markovian approach.

Keywords: Enzyme kinetics; Stochastic reaction chain; Random walk; Steady-state

Domains: Physics [physics]; Physics [physics]; Chemical Physics [physics.chem-ph]; Chemical Sciences; Theoretical and/or physical chemistry

Denis Michel, Philippe Ruelle. Twelve competing ways to recover the Michaelis-Menten equation reveal the alternative approaches to steady state modeling. Journal of Mathematical Chemistry, 2013, 51 (9), pp.2271-2284. ⟨10.1007/s10910-013-0237-5⟩. ⟨hal-00920806v2⟩