Legitimacy of the stochastic Michaelis-Menten approximation.
Michaelis-Menten kinetics are commonly used to represent enzyme-catalysed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of traditional differential equation models. The presence of small concentrations in biochemical systems, however, encourages the conversion to a discrete stochastic representation. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and that the validity conditions are the same as in the deterministic regime. The authors then compare the Michaelis-Menten approximation to a procedure called the slow-scale stochastic simulation algorithm (ssSSA). The theory underlying the ssSSA implies a formula that seems in some cases to be different from the well-known Michaelis-Menten formula. Here those differences are examined, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis. This exercise serves to place the conventional Michaelis-Menten formula in a broader rigorous theoretical framework.
University of California Santa Barbara, Department of Computer Science, Santa Barbara, USADan T. Gillespie Consulting, Castaic, USA.
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Sanft
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Gillespie
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Petzold
D000465:Algorithms; D004798:Enzymes / Q000378:metabolism; D007700:Kinetics; D008956:Models, Chemical; D008962:Models, Theoretical; D013269:Stochastic Processes
D004798:Enzymes