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A kinetic analysis of coupled (or auxiliary) enzyme reactions

preprint
revised on 19.08.2018 and posted on 20.08.2018 by Justin Eilertsen, Santiago Schnell
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 slow, the quasi-steady-state dynamics are governed by two fast variables and two slow variables, and when the indicator reaction is fast, the 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.

Funding

This work is partially supported by the University of Michigan Protein Folding Diseases Initiative

History

Email Address of Submitting Author

schnells@umich.edu

Institution

University of Michigan Medical School

Country

USA

ORCID For Submitting Author

0000-0002-9477-3914

Declaration of Conflict of Interest

No conflict of intrerest

Licence

Exports