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Legitimacy of the stochastic Michaelis–Menten approximation

Legitimacy of the stochastic Michaelis–Menten approximation

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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.

References

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      • D.L. Nelson , M.M. Cox . (2005) Lehninger principles of biochemistry.
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      • L. Michaelis , M.L. Menten . Die kinetik der invertinwirkung. Biochem. Z. , 333 - 369
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