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Phase-Plane Geometries in Coupled Enzyme Assays

revised on 19.09.2018, 13:37 and posted on 19.09.2018, 13:46 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. 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, the dynamical behavior of coupled enzyme catalyzed reaction mechanisms is studied by analysis of the phase-plane. We analyze two types of time-dependent slow manifolds - Sisyphus and Laelaps manifolds - that occur in the asymptotically autonomous vector fields that arise from enzyme coupled reactions. Projection onto slow manifolds yields various reduced models, and we present a geometric interpretation of the slow/fast dynamics that occur in the phase-planes of these reactions.


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).


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University of Michigan Medical School



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Declaration of Conflict of Interest

No conflict of interest