Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios.

*(English)*Zbl 0714.92006Summary: We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.

##### MSC:

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |

80A30 | Chemical kinetics in thermodynamics and heat transfer |

65L99 | Numerical methods for ordinary differential equations |

##### Keywords:

Michaelis-Menten approximation; scaling; fast and slow timescales; double intermediate enzyme-substrate reaction; ratio of initial enzyme to substrate concentration; quasi-steady state assumption
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\textit{C. L. Frenzen} and \textit{P. K. Maini}, J. Math. Biol. 26, No. 6, 689--703 (1988; Zbl 0714.92006)

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##### References:

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