Phase-Plane Geometries in Coupled Enzyme Assays

19 September 2018, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


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.


Enzyme kinetics
Coupled enzyme assays
Michaelis-Menten reaction
Time-dependent slow manifold
differential-algebraic equations
asymptotically autonomous vector field
Biological Sciences
Sisyphus manifold
Laelaps manifold


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