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A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions

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Abstract

As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis–Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis–Menten equations. Moreover, we show that when the indicator reaction is fast, the quasi-steady-state dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis–Menten equations, are derived. The theory can be extended to deal with more complex sequences of enzyme-catalyzed reactions.

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Notes

  1. It is of course possible to demand a more restrictive inequality by setting \(\lambda \delta _S \ll 1\).

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Authors and Affiliations

  1. Department of Molecular and Integrative Physiology, University of Michigan Medical School, Ann Arbor, MI, 48109, USA

    Justin Eilertsen & Santiago Schnell

  2. Department of Computational Medicine and Bioinformatics, University of Michigan Medical School, Ann Arbor, MI, 48109, USA

    Santiago Schnell

Authors
  1. Justin Eilertsen
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  2. Santiago Schnell
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Correspondence to Santiago Schnell.

Additional information

This work is partially supported by the University of Michigan Protein Folding Diseases Initiative, and Beilstein-Institut zur Förderung der Chemischen Wissenschaften through its Beilstein Enzymology Symposia. We are grateful to Dr. Antonio Baici (University of Zurich) for helpful discussions about this work during the 2017 Beilstein Enzymology Symposia (Rüdesheim, Germany). We are also grateful for the insightful comments made by the anonymous reviewers, particularly Reviewer 1.

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Eilertsen, J., Schnell, S. A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions. Bull Math Biol 80, 3154–3183 (2018). https://doi.org/10.1007/s11538-018-0513-4

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  • DOI: https://doi.org/10.1007/s11538-018-0513-4

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