### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 58-69 |

Number of pages | 12 |

Journal | IET Systems Biology |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

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## Cite this

*IET Systems Biology*,

*5*(1), 58-69. https://doi.org/10.1049/iet-syb.2009.0057