These are preliminary reports that have not been peer-reviewed. They should not be regarded as conclusive, guide clinical practice/health-related behavior, or be reported in news media as established information. For more information, please see our FAQs.
sm_5-preprint.pdf (500.01 kB)

Phase-Plane Geometries in Coupled Enzyme Assays

submitted on 25.02.2018, 02:47 and posted on 26.02.2018, 14:28 by Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. The dynamical behavior of couple enzyme catalyzed assays is studied by analysis in the phase plane. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course expressions valid under the quasi-steady-state and reactant stationary state assumptions. In this paper, we analyze two types of time-dependent slow manifolds that occur in asymptotically autonomous vector fields that arise from enzyme coupled assays. We show that the motion of the slow manifolds relative to the motion of the solution must be taken into account in order to formulate accurate leading order asymptotic solutions. We also develop a rigorous mathematical framework from which to analyze enzyme catalyzed indicator reaction from couple enzyme assays.


This work is partially supported by the University of Michigan Protein Folding Diseases Initiative, and Beilstein-Institut zur Forderung der Chemischen Wissenschaften through its Beilstein Enzymology Symposia. WS is a fellow of the Michigan IRACDA program (NIH/NIGMS grant: K12 GM111725).


Email Address of Submitting Author

Email Address(es) for Other Author(s)


University of Michigan Medical School



ORCID For Submitting Author


Declaration of Conflict of Interest

No conflict of interest